Let's think about the characteristics of Lila Mae and how they might relate to other characters in African American literature. Lila Mae is marginalized by her race, sex, and her ability to "intuit" mechanical problems rather than solve them empirically. She is a loner who fights the social and political system that impedes her upward mobility.
Another character in African American literature who might connect to Lila Mae is Anyanwu in Octavia Butler's novel Wild Seed. Like Lila Mae, Anyanwu has special magic powers that distinguish her from the other characters. Like Lila Mae, Anyanwu struggles against patriarchal systems and seems much more intuitive in her relationship to animals (as Lila Mae is with her intuitive connection to elevators).
Jessie Fauset's novel There is Confusion also features an ambitious female protagonist who comes into conflict with racist and patriarchal systems.
Toni Morrison's Song of Solomon is another book that features the intuitive, spiritual powers of a female character (Pilate) that contrast with the materialism of Macon Dead. This juxtaposition could well correspond to that of the Intuitionists and Empiricists in The Intuitionist.