Let's move is absolutely okay to be used. It just depends on the context of usage, and on a personal note, it also depends on the relationship that you have with the people you use " Let's move" on. My answer is very similar in it's premise to that of J.R's comment.
Lets move is basically used in a commanding tone, so it does not have to be associated with the military but coaches of sports/athletic teams use it often as well. Generally, lets go can be interpreted as a request and let's move can be interpreted as a command.
"Please lets go or lets go please " is perfectly valid while " Please lets move or lets move please " sounds kinda funny.
So discussing your question. When you use it on your friends who are distracted from the goal (which is going to the movie) is perfectly valid, I myself end up stuck at the snack bar whenever I go to the movie to it takes a " lets move!" from my friends to get my ass out of the snack bar premises. So maybe you made plans for a movie and your friends end up playing black ops, counter strike, then a "lets move" is completely warranted and justified because the command "lets move" translates into a good natured " move your ass off the couch, we got a movie to catch" and that is fine. On the other hand, f you are going to the movies with just acquaintances or colleagues, then a requesting tone is appropriate so "lets go" would be more appropriate.
On a lighter note, trust me, when I am hooked to a game or a roadside snack, dragging me away from there is a mission. Hope it makes sense.
There is something else, sometimes people say " let's make a move" meaning to say "well, lets leave/move from here" I have heard my colleagues say "let's make a move then " when we go out for lunches or dinners and we are done eating. I don't know if it is related to the question, but I thought I might mention it.