The way mold grows is, a spore has to land somewhere moist, i.e. with at least a tiny amount of liquid water on it. So if you want to keep stuff like fresh berries in the fridge for many days, the best thing to do is not wash them right away, but instead leave them with a nice dry outer surface. That way, even though they're obviously full of wet juice inside, they'll last longer because if a spore lands on the outside, it doesn't have access to enough water to grow.
That said, you're typically storing lettuce in the fridge for a few days at most, and one of the other ways to keep stuff fresh in the fridge is by having it completely submerged in water. If a mold spore lands on the surface of clean water it's also not likely to prosper, because it needs nutrients as well as water. This is why if you have sauer kraut or something, you should make sure to push all the vegetables down into the brine (I mean, the salt obviously helps quite a lot there but it's the same basic principle.)
Basically mold grows fastest where there is moisture/condensation on the surface of food - either drier or more water-logged conditions can slow it down.
I've never actually stored lettuce the way you're describing, but I have stored fresh herbs that way and it works great. Herbs completely submerged in water last a while (over a week) and seem perfectly safe, so why not lettuce?