Lester is basically the narrator throughout the entire film. And, overall, the storytelling and narration is pretty straightforward: Lester takes us through the last year of his life, and we get a pretty comprehensive view of all the wonderful and horrible stuff that leads up to and/or causes his untimely demise.
Pretty straightforward, right? One interesting thing to note, though, is that the film begins with a clip of Jane asking her boyfriend to kill Lester, and the movie kind of builds suspense and mystery about how Lester will die and who will kill him (because we know from the very beginning that he will die).
Is it Carolyn, the frustrated wife who doesn't want Lester to "get away" with the adolescent behavior that went part and parcel with his big life transformation? Or is it his daughter, Jane, who's grossed out by Lester's lust for her friend? Or is it Ricky, Jane's boyfriend, who seems just unhinged enough to do something like murder?
Turns out, it's none of the above—Ricky's dad ends up being the killer—but we bring all this up because the whole suspense angle seems a little surprising, given that this is mostly a family drama. The murder mystery stuff is probably a remnant of the original script, which began and ended with Ricky and Jane on trial for Lester's murder. Even though that specific plot point evaporated, maybe these small examples of building (unnecessary?) tension are just the remains of that earlier focus of the film.
P.S. The idea of the movie being narrated by a dead man stems from Sunset Boulevard.