Great question — answering as the UphillTech team:
Spoiler It's pretty obvious from the blood on Fitts that he was the shooter. Also, there is a shot near the end of the film that shows Fitts' gun case sans a revolver which is seen earlier. These combined make it clear that Fitts is the shooter. Fitts believed that Lester was his son's gay lover. You may recall that there is a scene where Fitts sees his son and Lester in Lester's garage through the garage window, in what appears to be a compromising position. In fact, Fitts' son is merely rolling a joint while Lester reclines in a chair.
Full answer by Johnny Bones: https://movies.stackexchange.com/a/52398 (CC BY-SA 4.0).
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