we have garden blankets which basically live outside. they are usually wool blankets which will easily dry out and they seem to handle being outside most of the year. we do have to remove them during the day, however i have kept them on over wintering brassicas for a whole month with no ill effect.
sometimes they are old wool blankets or an old wool blanket which got some funk to it, like mould.
These have been found for free at our local free store. however i imagine buying them at second hand stores would also work if the price was right.
When I use sheets to cover my chicken tractor, rain drizzle drips in one spot. It may pool in that spot. But you could always water other dry areas.
I think it might be too dark for lettuce unless it is a thin, light color cloth. But I'm in Texas. I might use them for excluding butterflies that lay caterpillar eggs on lettuce, or to keep the lettuce a little cooler. Maybe spraying water on the cloth would keep that area cooler due to evaporation. But it would be a lot of spraying.