My husband is from a more rural area then I am. I have always bought lettuce brought it into the house, cleaned the whole head, sometimes wrapping in papertowels until the water drains and it stays crisp. My husband thinks you should put it in the fridge dirty and wash the leaves as you need them.
Certified GKH Gardening Expert
It's better to wash it first and then store. This article should help you: https://www.gardeningknowhow.com/edible/vegetables/lettuce/cleaning-lettuce-how-to-clean-and-store-garden-lettuce.htm