Portraying a real person, she said, is “a blessing and a curse,” because, on the one hand, “we get to meet her and see her and talk with her and experience the way she thinks about things,” but, on the other hand, “we have to honor her in a way, so there’s a little bit of pressure to make sure that we’re doing it right.”

Ms. Lucas, who last year became the youngest person to win an Obie Award for her portrayal of Little Alison, expressed similar concerns, saying, “Sometimes I wonder if I’m acting the way she acted.” Ms. Lucas has tried to extract ideas from the book (which she read, at age 9, “with my mom covering up pages that I wasn’t allowed to see”) and by searching for similarities to her own experience.

“I know she definitely hated dresses and stuff like that,” said Ms. Lucas, who is now 11. “I’m actually sort of like Alison, because first of all I have two brothers, and I really love to draw, like she does.”

Few musicals arrive on Broadway with as many thematic challenges, or as much praise, as “Fun Home.”

The subject matter, obviously, is a complication in a Broadway market dominated by lighter material. The show’s producers, Kristin Caskey, Mike Isaacson and Barbara Whitman, who raised $5.2 million to finance the Broadway transfer, are emphasizing the father-daughter relationship and journey of self-discovery, rather than the sexuality, the suicide or the fact that Alison’s father ran a funeral home (“Fun Home” was the Bechdel children’s nickname for the business).

The children create moments of jollity (one fantasy number echoes the Partridge Family), even in a home with pain and sadness. So the show’s marketing campaign suggests family — its logo features the frame of a house, with a Bechdel father-daughter silhouette in a window — and retro colors and typography inspired by board games of the ’60s and ’70s.

Pedigree is a plus: Last year, Ms. Bechdel won a grant from the MacArthur Foundation, and the musical was a finalist for a Pulitzer; its premiere, at the Public Theater in 2013, was greeted rapturously by critics — Ben Brantley in The New York Times called the show a “beautiful heartbreaker” — and it swept the Off Broadway awards season.