I always assumed that Lois lived with Ellen until she was an older teen, and that she probably argued with her mother and went to live with Sam.
It's certainly possible that Ellen divorced when Lois was twelve, but didn't quit drinking until she was fifteen.
Maybe that's why Lois left to live with her father.
Don't forget too that she was an exchange student in Ireland for a while too, so she wouldn't have lived with either parent then.
