Trying to overwinter water lettuce in cold regions is usually more hassle than it’s worth. They are cheep enough and grow fast enough during the summer that it is usually easier and more cost effective to buy new ones each spring.
If you want to try keep lettuce over winter it needs a warm spot that is brightly lit, artificial lighting may still be necessary. Fluorescent shop lights 6” above the plants is about right. Some people have reported success by putting a couple inches of compost in the bottom of the container the lettuce is in. Others actually pot the lettuce and submerge the pot so the rim is an inch or two below the water surface.
That's some info from trusty google .
I do belive it can be kept/grown in a tropical fish tank? So if you have one, chuck some in over the winter and remove it after the winter?