Buy it as late as you can. Keep chilled.
Clean it well the night before you leave and wrap in damp paper towels. Keep chilled.
Pack gently in a cooler where it won't get crushed - and Keep it Chilled.
Saturday (usually) morning - while you've got some time, put the lettuce and/or parsley in some ice water to "crisp". Then dry it with paper towels and make up the four boxes - you'll tweak it some but do this while you've got some time. Then put the boxes back into a cooler with some ice to keep chilled.
Just my opinion - you're mileage will probably vary!