I support the previous educator's succinct assessment, but I'll elaborate on certain elements of the play which deal specifically with gender, as well as the play's relationship to the Black Arts Movement. Both are key in understanding the play's key message, which equates black assimilation with death. I'll begin with the latter.
In 1965, Amiri Baraka and Larry Neal developed the Black Arts Movement, which sought to develop art forms that spoke directly to the needs of Black America. This meant rejecting the canon, white authors who attempted to depict black people (e.g., Faulkner), as well as the books on which black people had been raised, such as the "Dick and Jane" series, and creating work that re-evaluated Western aesthetics in favor of centralizing the experiences of black people. It was key for black people to tell their own stories in their own ways.
Baraka wrote Dutchman in 1964, when he was still married to Hettie Jones, a white Jewish woman, and a part of the Greenwich Village Beat Generation scene. A year later, Baraka formed the Black Arts Movement with Neal and embraced both Communism and Black Nationalism. Two years later, he married a black woman--Sylvia Robinson, also known as Amina Baraka.
I mention all of this because Baraka was an artist whose work was an infused by his evolving politics, which also impacted how he lived his life. It is possible that he saw some of himself in Clay. Baraka was also middle-class--the son of a postal worker from Newark, New Jersey--and worked for The Village Voice in the early 1960s. He enjoyed many of the comforts that might be associated with his protagonist, Clay, but then began to question those comforts and, ultimately, rejected them in favor of activism. In this sense, Dutchman could be read as a morality play--a warning of what can happen to black people who attempt to fit into a system that is bent on destroying them.
The character of Lula is a thinly veiled modern Eve: Clay is destroyed by a white woman who is eating an apple. She assumes that Clay desires her and was looking at her through the window of the train car before she boards it. Baraka uses Lula to allude to the historical use of white women as objects of forbidden desire and excuses to murder and castrate black men, for real and perceived miscegenation, or interracial sex. However, Lula is not only an instrument of racist power, but a willing participant. She entices Clay, gains his trust, then murders him with the pocket knife that she uses to slice the apple.
Baraka seems to have viewed black men's attraction to and desire for white women as another facet of their assimilation and, again, a desire which could be deadly--both figuratively and literally. Some readers might, rather justly, perceive this interpretation of white women's role in society as sexist, for it is rather overt in its accusation that white women are untrustworthy and collude with...
white men to undermine black men. Others might, also rather justly, see the presence of Lula as an important commentary on how white women have helped to secure white male hegemony in the United States, in all aspects of life--social, political, economic, and sexual.