If you can believe Teddy's lies then he was a cop who had worked on the case of the break in, attack on Leonard and rape of Leonard's wife. He then worked with Leonard and helped him track down and kill John G. Teddy claims that he believed in Leonard and thought that helping him track down the killer would help Leonard feel peace. Now Teddy is an outside observer so he knows very well what Leonard's condition is, also since he was there since the initial investigation he knows how much Leonard has warped his own reality of what happened. So why is Teddy using Leonard?
Teddy seems to at the best be a dirty undercover cop (if he's even still a cop at all) at the worst he's a drug dealer(and may be the original John G.). He seems to be using Leonard to kill people whether it's some form of vigilante justice or just killing the competition it doesn't really make sense why he would use someone who not only couldn't be trusted from literally minute to minute but who also had to be led around and talked into every action. I can see the usefulness of a revenge obsessed man who has the perfect documented alibi of "I can't remember what I did or who I was with", but it seems like a lot of effort and patience for not much payout. Is Teddy getting some actual satisfaction from making Leonard happy or does Leonard just amuse Teddy? Does Teddy even feel like he needs to help Leonard?
I'm asking why does Teddy help Leonard?