How does Jimmy know who Leonard is? [SPOILERS]

Just watched this again recently and it made me think; how does Jimmy know who Leonard is enough to call him "Memory Man?" We never see the events previous to Jimmy's death (not counting the motel phone scenes) so we don't know how long Leonard has been around or what he's been up to.

Jimmy is on edge when he arrives at the meet but his demeanour changes when he discovers it's Lenny there instead of Teddy. Why? Because he knows him well enough to not be a threat, enough to be friendly with and joke about.

I read on another thread that Burt (The Motel worker) was working for Jimmy and that Jimmy was the owner of the Motel Leonard was staying at. Burt confesses to Leonard that he is renting out 2 rooms to him after telling his boss of his condition. So this could be how Jimmy knows who Lenny is but not necessarily what he looks like so they must have met previously for Jimmy to know what Leonard looks like but Lenny doesn't have a polaroid of Lenny so he didn't consider him a friend...?

Also, Natalie knows who Lenny is as she's heard of him from Jimmy so Leonard and Jimmy must have had enough encounters for Jimmy to tell his girlfriend about but yet she'd never met Lenny before the first time he went to the Bar after killing Jimmy.

I know it's irrelevant to the story really but I love the film, I think it's a classic I like analysing films. It just makes me wonder where Lenny was right before we meet him, how far he's come from the original head injury, who he's killed and how long he's been in the current area as seen throughout the film.