Lettuce can be problematic to store for more than a few days. You eventually get that slimy mold, and leaf wilt.
I happened to remember that you can clone plants by cutting off a branch and sticking it in some dirt or water. In a week or so roots will begin to grow from the place it's cut off. Until the roots begin to grow and take up water, however, you have to keep the leaves from drying out, either by constantly spraying them, or you can put a plastic bag over the plant. If you do that, you have to cut some slits in the bag so air circulates, otherwise that slimy mold will grow on the leaves.
After a week this is what I have. I haven't had to add water. The lettuce looks good. The leaves are kind of dry to the touch. They almost don't feel dry because they are kind of cool and flexible, like a plant growing in the garden, I guess. There's no slime on them at all.
Sometimes things work out and I'm elated.
I just used an old bag that a loaf of bread came in. I'm too cheap to buy plastic bags when so many things come in plastic bags now and you see so many plastic shopping bags blowing in the wind.