In Angela's view, "beauty" is a kind of strength. The beauty she pursues is essentially the power to put herself above all sentient beings. It can be seen that two people are not tied together for pure sex, but are "opportunities" for each other to change.
The film seems to show that beauty is freedom, a soul that breaks imprisonment, and an unrestrained soul. However, Lester was finally shot, even though he had just escaped from the ugly world and just realized the beauty of life.
It seems that the real "American beauty" is beyond our reach. We can only dream of waking up in our dreams.
The director is very clever and doesn't dwell too much on this "neither fish nor fowl" relationship. It becomes a lead, of moderate length, and ends in time at an appropriate time-that is, there is no real sexual relationship between Lester and Angela. That's the point. Before having sex, everything is tolerable and controllable. Once you have sex, this dangerous adultery is bound to start a prairie fire.