Lauren is totally the daughter of a preacher man: Reverend Olamina.
We never learn the dude's first name in Parable of the Sower, but that doesn't mean he's not important. In fact, the book opens on his 55th birthday on July 20, 2024. Dude's an older gent, and he's totally a Baptist preacher. He's also a professor and a dean; that makes him a source of income for Lauren's family (2.26). Plus, he's a respected leader of Lauren's hometown community of Robledo, a small place he was eager to abandon as a young man (2.19) but has come back to.
Basically, dude's got a lot of authority. But what impact does that have on Lauren, our protagonist?
While Lauren does respect her father and admire how he leads her community—she takes his side over Keith's, after all, when the two are at odds over Keith running away (10.51)—not even Reverend Olamina can make Lauren into a completely obedient child. Sure, he leads the target practice sessions (4.28), gives sermons (6.8), and more, but as we all know, Lauren is headstrong.
Reverend Olamina doesn't always do so perfectly himself. His relationship with his son Keith is all messed up, since Keith runs away from Robledo and into danger—and blames it on his father (8.42). The Rev fights with Cory, Lauren's stepmother. But again, he does seem to try as much as he can, and he does pretty well at it, so we'll say Lauren has a good role model in him. His own life has been pretty tough, after all: his parents were murdered (2.19), and Lauren's mother died in labor.
Anyway, remember the recurring dream the novel opens with, in Chapter 1? Lauren says she has unsettling dreams when she tries "to be my father's daughter" (1.1). Ultimately, Lauren can't follow in the footsteps of her dad and be successful. She can't be his daughter 100%. He's a religious leader, and she's a religious leader, sure, so they have a lot in common—but "A tree / cannot grow / In its parents' shadows" (7.Verse4.1-3), as Lauren puts it. She ultimately has to separate from him.
It seems that fate held their separation in store, because Lauren never actually has to abandon her father of her own volition; it happens on its own. Dude mysteriously disappears at age 57 (13.6-7), probably captured and killed by wrongdoers beyond Robledo's external wall. The loss of income wreaks havoc on the Olamina family, but things quickly go from bad to worse when Robledo is destroyed entirely not long afterward. Frown.
All in all, Reverend Olamina seems like a man who wants to do the right thing and help people, but he's not someone who can fully understand and guide Lauren. She's just too much her own person. He does try, even going so far as to discipline her with physical beatings (10.47) and lecture her about how to properly alert others—such as Joanne—to danger (6.67), but in the end, Lauren takes charge of herself. It's not his job.