Because
Patrick Jane is a shadow of a man.
Once upon a time, he was a man. Cunning and deceitful, but still a man—a good man who loved his family in the fashion of all good men. That is to say, he loved them totally, he loved them completely, he loved them so that they were his world, reason, and life. When they were taken from him, Patrick Jane, the man, was left with heaps of ill-gotten nothing and a shredded soul. His heart broke, his conscience died, and he was left, cruelly alive with nothing to live for.
Except death and a debt to be paid.
So now Patrick Jane, the shadow, uses that cunning and deceit to bring himself closer to paying that debt and closer death. He smiles and jokes and speaks like the man he was. He works closely—poorly, but then he never was well socialized—with a group of good people, who he thinks he cares about, and who he knows care about him. Some days he thinks he might just live, just a tiny, teensy little bit for them, too.
Because he sees in Rigsby a world of good and potential—the kind of potential Patrick Jane might have had once, long ago, before he became part of his father's grifts—and he wants to make sure Rigsby continues to grow into the good strong man he deserves to be. Patrick Jane wants to see that, and he wants to know that he had a little part in making it happen. He wants the right to be proud of Rigsby.
Because van Pelt is the closest thing he has seen to an angel since he said goodbye to his wife and daughter the morning of the day they died. She is beautiful and patient and soothing. She cares for people. She cares for every single person that they see to as a result of their line of work, and she hasn't faltered. She hasn't cracked under the weight of all that sadness and negativity, and Patrick Jane hopes that never changes. He wants to notice when the nightmares get too hard and the job gets too sad because van Pelt should never have to give up on giving a damn to keep doing her job.
Because Cho is Batman only better. He does whatever he has to in order to protect people. He does it for a government paycheck with government resources. And he does it to atone, unlike the vengeful Dark Knight. It's a dedication and determination Patrick Jane can't help but admire because, while it has occurred to him to atone for all of the lies he has told, vengeance is the stronger motivator. So Patrick Jane gladly plays Robin and Alfred and Gordon and Batgirl—any and all characters that Cho might need—because Patrick Jane wants Cho to forgive himself for his wrong doings, perceived and actual, in the way Patrick Jane can only hope to do for himself one day.
Because Lisbon is terrible at having fun. With all of the heartache and responsibility foisted on her as a child, and her insistence at being the best she possibly can be as an adult leaving her, once again, smothered by responsibility, Patrick Jane doubted Lisbon had ever properly learned to enjoy life. So he teases her, jokes with her, and generally just bugs her until she gives in and laughs because she deserves, more than most, to have a little fun and Patrick Jane wants to help.