Same with a burger. Your lettuce should be dry (pat it with a paper towel if you must) and put it as the bottom layer. This creates a moisture barrier that stops your bread/bun from turning into a soggy mess.
On a sandwich, the cheese should be on the other side for the same reason. Keep all the wet stuff from turning your bread into slop.
Absolutely correct on all accounts. These are important laws, and many of us have independently arrived at them due to previous errors in sandwich construction.