I’m up here in MA so winter lettuce would be impossible although I never thought to try doing it indoors.
It grows a little elongated indoors, but tastes great! I use the natural sun and add a grow light for a couple of hours after sunset, and sometimes on gloomy, dark days.
Outdoors in your area, I think you could do it using a hotbed that is covered, but then I am such a pansy, I would avoid getting the lettuce because I would not want to go out in the cold.LOL