“She sat down, stubbed out a cigarette, tossing her long hair and from then on I watched her expecting something — I didn’t know what. Apparently she did not eat, nor did she clap for any of the other speakers. She smoldered and smoked.”

That passage is First Lady Lady Bird Johnson’s description of Eartha Kitt at a White House luncheon — a meal that would come to define both women’s legacies — from her White House diaries, a meticulous account of Lyndon B. Johnson’s five years as president. As shown in “The Lady Bird Diaries,” a gorgeous and haunting new documentary from Dawn Porter (“John Lewis: Good Trouble”), the First Lady was right to expect something.

Recreated thanks to an uncanny combination of Lady Bird and Kitt’s own voices, footage filmed at the event, and evocative illustrations from Molly Schwartz, we see history come to life as...