The contrast between the Lisbon who is supposedly so by-the-book and the Lisbon we see who often gives Jane such a surprising amount of latitude, got me interested. This is the result. Once again, these are my own theories and should not to be confused with what the actual owners of these characters may think about their creations.
Teresa Lisbon had given her team strict instructions. Patrick Jane was never allowed to go off and investigate by himself. If she wasn't with him herself, then one of her agents must accompany him. No exceptions.
The team considered this a drag.
Cho thought it a bit demeaning being reduced to following their consultant around to make sure he didn't do anything too stupid. Like he'd be able to stop him, anyway. It wasn't so bad when Jane included him in what he was doing, but usually he preferred to be cryptic and play his cards close to his chest ("If I tell you how it's done, the magic circle will send a team of assassins to kill us all. It's the law."). Which meant that Cho was there just to babysit, which was definitely not what he'd signed up with the CBI to do.
Rigsby felt that the time he wasted following Jane about could be much better spent either:
a) Being wherever Grace was;
b) Doing his actual job and possibly, during the course of doing his own investigative work, finding something that would impress his boss; or
c) Eating.
Granted, Jane was usually easy-going about stopping for food once he'd finished doing his thing ("Don't take too long. I'm hungry."), but it was still not a chore Rigsby was partial to.
Van Pelt found Jane embarrassing. He was embarrassing even when he wasn't specifically trying to be; but since he knew how much she hated it, he naturally went out of his way to find new ways to make her cringe ("Don't embarrass me." "What do you mean?" "You know what I mean!" "No, what do you mean?" ... "Okay, that's what I mean!"). Which meant that Van Pelt disliked being stuck alone with Jane so much that she sometimes actually whined about it to her boss. Lisbon, while mildly amused by this, nevertheless did not relent.
Jane, for his part, derived substantial amusement from spending time with each of his colleagues one-on-one and he enjoyed dragging them into his schemes and observing their reactions. Nevertheless, he really didn't see why they needed to be there all the time. He was a grown man, for pity's sake. Some of his more delicate missions needed to be carried out solo, without an unimaginative cop lurking nearby, cramping his style and dragging the law into everything.
The three agents, when none of them had been specifically ordered by Lisbon to accompany Jane, worked on a strict rotation. The two whose turn it wasn't were always smugly relieved; the one whose number was up would take responsibility for the wayward consultant with gloomy resignation. If Jane somehow gave them the slip, however, they became slightly panic stricken, like they'd lost someone's child. They hated having to go to Lisbon and tell her that Jane had gone off unsupervised ("Um, don't get mad, but..."). It was always a sure-fire way to get her annoyed and worried.
For the most part, Lisbon took Jane with her (and vice versa). Lisbon did not consider this a drag. Nor did Jane. They actually made an excellent team. They bounced ideas off each other. They helped improve each other's (noticeably different) thought processes. They spent so much time in each other's company that they had now mastered the art of near-perfect non-verbal communication. Lisbon usually did all the routine, yet crucial, things that a cop is required to do to make a case. While she was keeping witnesses and suspects busy in this way ("Reality check, Jane, I'm your supervising agent, not your decoy!" ), Jane snooped ("getting the lay of the land", as he put it). His snooping usually turned up something interesting, at which point he would bellow for Lisbon to come and do her cop thing. Or he'd get punched in the face or held up by a gunman (or some other variation on this theme) and she'd come and rescue him ("I would rethink this new technique of yours!"). It was like a relay race. They needed each other. They were better together than separate.
Lisbon enjoyed Jane's company for several reasons.
First, he amused her. As far as she was concerned, that was a good enough reason on its own to keep someone around.
Second, he could do things as a consultant that she couldn't do as a cop, but wished she could. Not that she would have ever admitted this in a million years. Even under torture. Of course, Jane knew this, and Lisbon knew that Jane knew. Though it sometimes made him even more unmanageable, this knowledge was necessary for them to work effectively as a team. And since she could never have told him, it was an example of one of those occasions when his ability to read people (her) was actually rather useful. A large part of their non-verbal communication revolved around him doing things for her that she could not appear to be sanctioning. They had an understanding – he would do something outrageous, knowing that she wouldn't mind. She would pretend to get annoyed and disclaim responsibility on behalf of the CBI ("I apologise. Mr Jane is a consultant. His statements in no way reflect the official view of the CBI."). If the situation called for it, he would pretend to be sorry. They would get results, or at the very least the gratification of bringing some idiot down a peg or two. Everyone was happy. Well, everyone besides the aggrieved party (there was always one of those), Minelli ("I'm very disappointed and I'm embarrassed. How could you do this to me?"), the Attorney General, and anyone else who had to do extra paperwork as a result. Of course, the downside of this meant that Jane also got away with doing a great many things that she most definitely did not want him to do, but her genuine anger on such occasions helped her give a more convincing performance the rest of the time. There's always a silver lining.
Third, she enjoyed teasing him. Nothing was as much fun as getting Jane on the back-foot.
Fourth, she liked him. And she knew he liked her. They got on well. Most of the time, anyway.
Jane also enjoyed Lisbon's company for several reasons.
First, she was very pretty. Beautiful, even. He liked looking at her. A lot.
Second, she found him funny. There is nothing a man likes more than a woman who catches all his jokes, even the really obscure ones. In fact, she sometimes found him funny even when he wasn't trying to be. He chose to find that flattering. There's a lot to be said for making a lovely woman laugh, even if she sometimes laughs at you rather than with you.
Third, he found her sharp wit very amusing. And he liked the mischief that lurked not terribly far below the surface of the serious agent. He liked that he knew how to bring this side of her out, even when she didn't think it was appropriate. She found it hard to resist teasing him.
Fourth, she didn't suffer fools gladly. She was often itching to knock some annoying, self-important moron off his high horse, and he knew she derived deep satisfaction from him being able to do it instead. Not that she would ever admit as much, of course, but that was a part of their game. A game they both enjoyed tremendously.
Fifth, she was complicated and interesting. She kept huge parts of her personality carefully hidden for the sake of her work and her reputation, but he knew how gratifying it was for her to sometimes allow these parts of her to live vicariously through him. People found it hard to understand how someone as by-the-book as Lisbon appeared to be could put up with a loose cannon like himself. The answer was simple really. Lisbon was not nearly as by-the-book as she appeared. She was sensible, intelligent and careful and, while acknowledging its imperfections and limitations, she believed enough in the law to act as its faithful agent. But imperfections and limitations it still had, and there were times when this really grated on her. Sometimes her personal opinion on a matter had nothing in common with her official opinion on it. She was not a person who liked subterfuge, so this did not sit well with her. She was always so tightly wound and controlled because it took a great deal of effort and self-control to keep hidden all the parts of her that were unhelpful in her work.
Her rebelliousness.
Her gentleness and empathy.
Her mischievous streak.
Her kindness.
Her irreverence.
Her wish to sometimes have the chance to act without thinking, leap without looking, react with no thought for the consequences, take ridiculous risks.
Her quirkiness.
Her desire to just relax and let someone else take responsibility.
Jane saw and liked all these subterranean parts of her. In his opinion, it was all hidden treasure.
Sixth, she understood him. She really saw him – not just the image he projected, but also the broken mess he hid. And she still liked him and appeared to want him around. That made Patrick Jane smile every time he thought of it.
So, although at times Jane drove Lisbon up the wall, she always found the view from up there very interesting.
And although Lisbon kept an constant eye on Jane, either in person or by proxy, as though he was five years old, at least he could never complain that he wasn't being seen.
Out of courtesy, Jane saved his more dramatic and potentially damaging exploits for when Lisbon wasn't there ("That's why I didn't tell you. You have total deniability."). There is only so far you can bend someone, after all, before they break.
The trouble usually started because Jane's narcissistic streak meant that he wanted to figure out 'whodunnit' mostly to satisfy his own personal curiosity, rather than to bring the perpetrator to justice. Which meant that he used any means possible to do so, however inappropriate, stupid or illegal. And he often tricked or manipulated his team-mates into helping him, usually by exploiting their confusion as to whether they were following Lisbon's instructions by staying with Jane, or disobeying her by not stopping his plans. Once the damage was done, he then left it up to other people to fix the mess.
Lisbon, on the other hand, had always sacrificed her personal preferences for the greater good. The hardships she had suffered in her life had taught her that the world did not revolve around her. Much of her inner strength came from her unselfish desire to protect others. Not only did she believe in protecting people's rights, but she also intimately understood the rules of evidence and the importance of her job in gathering untainted evidence for use in court. What was the point of catching the criminal if you did so in a way that ensured he couldn't be tried and would therefore go unpunished? She knew the difference between Jane shenanigans that simply caused trouble, and Jane shenanigans that could ruin a case. The former she condoned (watching him toy with arrogant fat cats was actually endlessly amusing), the latter she did not. She knew that Jane knew the difference, because he tended to only do the latter when she wasn't around. Which infuriated her.
Sometimes when Lisbon was genuinely in a rage with Jane, she would punish him by repeatedly sending him with one of the others. He knew he was being ex-communicated. He would get a little hurt glint in his eye at first, but if she persisted for more than a day, he would start acting up. He would do things that only she could stop him from doing ("Control your man there, Lisbon"). He would get her attention and force her to engage. And forced to choose between her job and her grudge, she would always choose her job. Besides, she wasn't very good at holding grudges. That was more Jane's specialty. And once he'd punished her for abandoning him by getting her into trouble ("What were you thinking leaving this man alone at an event like that?"), they would be prickly and irritable with each other for a while and then she'd let it go. She really was hopeless at grudges.
To apologise, he would find a way to make her laugh. Or at least smile. Sometimes just with her eyes, but it was enough. She always forgave much too easily. Unforgiveness was also more Jane's specialty.
Lisbon believed in leading by example, though. There may be things that you can't fix, but you'll never know till you try. And hope is a wonderfully tenacious thing.