Hmm. Is your soil covered with snow? Any idea how frozen the soil is?
Yes, lettuce likes cooler weather. But a hard frost will take it out.
I'm in zone 6b and ground is frozen here. With about 6-8 inches of compressed snow on top. More cold weather coming this weekend means its going to be more than two weeks before our ground thaws.
I checked my garden notes from last year and I direct sowed spinach and lettuce March 15. But we had a warm early spring.