"Trust me, I need to write this down."
Leonard says this to a waiter while he is getting directions to his motel. The man tells him it's easy to remember, but with Leonard's condition he doesn't remember anything after a few minutes. The dramatic irony of this line is one of the few comic moments in the film, as we know that Leonard needs this, but the waiter has no idea.
"Please, call me Leonard. My wife called me Lenny."
Leonard asks Natalie to call him Leonard, as Lenny is solely reserved for his wife who used to call him that when she was alive. This alludes to the fact that Leonard has some trauma and a fraught relationship to his own past.
"You know what we have in common? We are both survivors."
Natalie says this to Leonard in order to create a connection between the two of them. Ironically, Leonard doesn't know that she is using him in order to "survive" her current situation. She is using him more than she is helping him, and yet her line is not entirely untrue; they are both survivors.
"So what am I doing? Oh, I'm chasing this guy. No, he's chasing me."
In the middle of chasing Dodd, Leonard has a memory lapse and forgets what is going on. He is in a high stakes chase sequence, but suddenly forgets what he is even doing there. In a somewhat humorous shift, he forgets where he is and what he is doing, and even who is chasing whom.
"You don't want the truth. You make up your own truth! Like your police file. It was complete when I gave it to you. Who took out the 12 pages?"
At the end of the film, Teddy reveals that he has been manipulating Leonard the whole time, but also tries to suggest that Leonard wanted it—that he doesn't want the truth. This is yet another way to manipulate Leonard into thinking that he is in control when he is clearly not.
"Memories can be distorted. They're just an interpretation, they're not a record, and they're irrelevant if you have the facts."
Because of the direness and intensity of Leonard's situation, he has to create a system to which he can adhere and trust. Here, he explicitly highlights that he can only trust the facts, even more than he can trust his memories. He suggests that memories are interpretations, and thus not as reliable as facts.
"You're not a killer, that's why you're so good at it."
After revealing to Leonard that he has been manipulating him, Teddy notes that the reason Leonard is such an effective killer is that he isn't actually a killer. Because Leonard has the purity of purpose of thinking that every man he kills is his wife's assailant, he is effective. This line reveals what a manipulative man Teddy is.
"I can't remember to forget you."
The tragedy at the center of Leonard's plight is that, even though he cannot remember what happened 10 minutes ago, he is unable to forget the attack on his wife and her death, a memory that haunts him constantly. He is addressing his absent wife when he speaks this line, expressing that, given his memory condition, he cannot even build on his memories enough to heal and move on. His grief is exacerbated by his memory lapses.
Natalie: What's the last thing that you remember?
Leonard: My wife...
Natalie: That's sweet.
Leonard: ...dying. I remember my wife dying.
This interaction speaks for itself. Natalie asks Leonard to describe when his condition started, when he stopped being able to remember things, and he tells her that it was when his wife died. There is also dark humor in this moment, because while Natalie thinks Leonard's memory of his late wife is a sweet one at first, he clarifies that it is much darker than Natalie suspects.
"I take it I've told you about my condition"
Leonard says this to Teddy in one of the first scenes of the film, which, chronologically, occurs at the end of the story. It shows that Leonard has memory lapses and cannot even remember whether he has met Teddy or what he has told him. Leonard is self-aware enough to guess that he has probably told Teddy about his condition, but he still needs to check.
