Black Comedy, Family Drama
Yes, American Beauty wears both the comedy and tragedy masks. On the sadder side of things, Lester dies just as life starts getting good for him again after years of apparent crumminess at home and at work.
And then there's the reason Lester dies: Frank is so ashamed of his own desire for men that he feels the need to kill Lester in an attempt (we assume) to make sure Lester doesn't talk. So at the movie's end, one man is dead before his time and another is driven to murder because he's ashamed of who he is. That seems pretty tragic to us.
Okay, but even acknowledging that big, bad, dark side, the movie is still pretty funny, even when it's making you uncomfortable. Take Carolyn, for example: when she first gets drunk with Buddy Kane, her whole attempt to suck up to him while hammered (read: she's having trouble stringing words together into sentences) is a little pathetic, but it's also hilarious. Plus, the comedy of the whole situation, and her willingness to make herself a little ridiculous to get some help from Buddy, kind of softens us toward her.
And that's really where American Beauty finds its "heart": in its ability to make us empathize with and care about characters even if we think their actions are ridiculous or even reprehensible. What's going on can be super sad, but the lightness and comedy infused into the plot often short-circuits any attempt to judge—when something's absurd, it's hard to jump too far into judgy-wudgy mode.
So really, all of this amounts to American Beauty being a black comedy focused on a family.