The mixed baby lettuce in the plastic bag may be a bit wet and/or stuck together because of how we wash it and then pack the bags into the boxes.
You should take it out of the bag, wash it in the big bowl (or just fill up the sink). Then 'spin dry' it, and store in an unsealed plastic bag in the fridge. In this condition, it should stay fresh for about a week.
If you don't have a spin drier, get one. It could be the best $10 you spend all summer.
The basic idea is that you want to keep the greens cool and moist, but not in standing water.