Who shot Lester Burnham in "American Beauty" (1999)?

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.

The film's original script makes it abundantly clear that Colonel Frank shot Lester.

INT. FITTS HOUSE - COLONEL' S STUDY - NIGHT

The Colonel enters, still wet. He's wearing LATEX GLOVES. Flecks of BLOOD cover the front of his T-shirt. He paces nervously in front of one of his GUN CASES; the GLASS DOOR is open, and a gun is conspicuously missing from inside. The Colonel suddenly looks down at the BLOOD on his T-shirt. He pulls the shirt off and wads it into a ball.

As to the question of whether Carolyn shot Lester, we know this isn't the case. Based on the fact that the gun found in the house (a 44 Magnum) was presumed to be the murder weapon, her gun (a Glock 19) simply doesn't have the same ammo.

The why is slightly harder to pin down. In short, the Colonel portrays a number of characteristics of homosexual self-hatred, repeatedly observing the joggers (and Lester) with evident interest, but then aggressively questioning his son when he shows what he perceives to be homosexual traits (he reacts very poorly when he sees the shower scene from Top Gun on his son's monitor, for example).

The Colonel doesn't respond. His eyes are focused on: On the TV: the shower scene from Top Gun plays. Seminude young MALE BODIES, artfully lit.

COLONEL: What the hell is that?

RICKY: [turns to the TV] Top Gun. It's about pilot training in the Air Force. You never saw it?

The COLONEL shakes his head, eyes glued to the screen.

The final straw appears to be the scene in which Lester is working out. Ricky comes over and rolls him a joint. The Colonel observes through the window and sees what he thinks is his son performing oral sex on Lester. He confronts his son who confirms that he's gay (and working as a male prostitute, no less). Frank throws him out of the house and then suffers what can only be considered a breakdown. The Colonel goes to Lester's house to confront him, only to then offer him sex, only to then be turned down. Faced with the ignominy of having 'come out' to Lester (and having been rejected) he decides to kill him, thus returning back to the status quo of having his sexuality be a secret.

Lester was killed by Fitts as I believe Colonel Fitts was gay himself.

Recall these moments from the movie:

1. Two men greeting Fitts; when they said they are partners, he asked several questions to clarify.

2. Fitts watching people jogging and asking, "Is that a gay parade?"

Finally, he kissed Lester in the garage thinking that Lester is also gay, but Lester denied Fitts.

Two things may have happened in the end:

1. Fitts grew insecure, fearing people will learn his secret - that he is homosexual - and killed Lester so that no one can know about it.

2. Fitts killed Lester because he was hurt by the denial of his love.