I add olive oil when the "bread" in question is going to be pizza, or (lots of) butter when it's going to be croissants, but I haven't been using oil at all in ordinary bread (which I've been baking roughly once a week). Although I usually mix in an egg or two to add protein, and eggs have some fat in them.

Sometimes I can get from feed to hot bread in 24 hours, but more often 36. Which may have to do with my sourdough culture's biome, or the weather, or the phase of the moon, or something.