Let is generally used for suggestion, proposal or permission.
Let’s go home.
Let’s do it.
Let + obj. (as subject) + v simple present form +obj.2 +extension.
Let’s= let us try again. Us is object but it is working as subject.
Let me do it alone.
Let him come in.
Let the man do his work.
Let the dog bark.
Let her listen to me.
Sometimes as permission / order
Don’t let them enter into the room.
Don’t let him come here again.
Don’t let her touch it again.
Let’s not is used in the negative sentence as jokingly
Let’s take the room. Let’s not!
Introduce as negative suggestion
Let’s not take the decision too early.
Let’s not start early.
Let’s not try again.
Don’t let’s start it again.