I can’t get it to germinate, but the place I have the seeds is similar to your description. Maybe the dirt isn’t rich enough or maybe lettuce can go in boxes. Arugula, on the other hand is growing like gang busters in the row over from the lettuce. I didn’t even thin the plants. It just keeps giving.
I sowed all of the different lettuce varieties directly into the salad table with the exception of Bronze Mignonette, which I planted in a seed starter tray. It is a larger head than the other leaf and Tom Thumb varieties. Need to free up some space in the salad table for it.
I recommend starting your lettuce in a rich seed starter medium (e.g. Miracle Gro Moisture Control). My lettuce seeds are germinating in just a few days. Alternatively, you may have a lame batch of seeds.