Lynne means well—she really does. Her desire to help the disadvantaged is sincere. Her desire to do good is sincere. But, no matter how hard she fights it, she's very much a product of her upbringing. You can run away from home, but that doesn't mean home won't follow.
Within the Movement, Lynne is an outsider in every possible way. Of course, there's the obvious—her whiteness—but that's just the start. She's a gosh-darned Yankee who wields her "Northern logic" like a blunt instrument (1.14.30). She comes from a rich family, even though she has given that all up. She's exuberant and helpful in a way that surprises and pleases her fellow activists—Truman especially.
Things come to a head after Truman and Lynne move to Mississippi. It's there that she finally admits, with great shame, that she believes that "the black people of the South were Art" (2.16.3). In other words, she sees them as objects (beautiful objects, but objects nonetheless) instead of people.
Later, after Tommy rapes her, Lynne pictures herself inside "a racist painting she had once seen in Esquire of a white woman [...] surrounded by black men" (2.22.18). Instead of seeing Tommy as an individual who did something unthinkable, he becomes representative of his race.
Life never gets better for Lynne. Her marriage with Truman deteriorates, her daughter is murdered, and she falls deeper into abject poverty. It's a sad story—but not one completely without hope. By the end, Meridian and Lynne are able to bond as sisters without race or class even entering the picture. It may not be a "happily ever after…" but it's the best we're going to get.