In this case you would not use Let's enter. Although "let's" is a contraction of "let us", when we ask someone to allow us to do something we say "let us" and not "let's". It would be confusing to say "let's enter" if we are telling someone to allow us to enter. "let's enter" would be heard as the equivalent of "entramos" o "entremos".
Let us play, please = déjenos jugar, por favor
Let's play, boys = jugamos muchamos.
Let's play, damn it, you guys, quit fooling around = juguemos, maldito sea, hombres, déjense de hacer los tontos
(I'm sure native speakers can do better.)
The children asked the teacher to let them play. We will now see whether or not he lets them.