The conflict in this wonderful play by Amiri Baraka is clearly the conflict between Lula and Clay, beginning with her seducing him, her racist comments, and clearly coming to a climax with the stabbing, and ultimate death of Clay. The racial tension is fraught throughout the play. Clay and Lulu are the only real characters in the play (the others on the subway play a minimal role), therefore the characterisation that you're looking for much be of them:
Clay is a typical bourgeois black male, so predictably bourgeois that Lula is able to tell his life history by the evidence of his dress (a too-narrow suit coat), his demeanor (decorous, tentative), and his style of speech (middle class, intellectual, full of pretensions).
The Caucasian Lula is a thirty-year-old femme fatale who alternately seduces and insults Clay. She is a mythical apple-offering Eve to his clumsy and naive Adam. Lula is the embodiment of Western Civilization, seductive and ferociously greedy, relentless, but also psychotic, lonely, trapped by her own cultural identity.