In the last episode of season 5, Lucille tells Lindsay that she is her half-sister. It could be possible that they have the same father but different mothers. For example, their father might have had Lucille with season 1 Nana but she left so season 5 Mimi raised Lucille and had Lindsay with the same father.

Yeah Mimi being Lucille's mother bothers me because of Nana in season 1. The show just tosses continuity out of the window. In season 1, the Narrator said that Tracey died 2 years ago in 2001, but in season 5, all of the sudden the Narrator says she died at the beach house 20 years ago in 1995-ish. For no reason at all, they just retconned it, with Michael and Gob talking about how GM didn't have a mother figure. Remember how in season 4 and season 5a, Sudden Valley had lots of houses with sex offenders in them? Yet suddenly in 5b, all the houses are gone except the model home and an empty lot where they start building their wall prototype. I wish they'd written Mimi as Lucille's sister instead.