A: Will your friend come to the party tomorrow?
B: Let me ask him.
I'm having trouble translating "let" here. Should I use "lassen" as follows?
A: Wird dein Freund morgen zur Party kommen?
B: Lass mich ihn fragen.
Your option works, but is not really idiomatic. A more idiomatic thing to say would be:
mal might also be replaced by a specific time: gleich, heute abend, ... If you are B and on the phone with said friend and A throws in the question, you might also say:
grade indicates that you are going to do it now, you might also use this sentence when you are about to pick up your phone and call or text.
I am sure there are more possibilities, I'll add them as soon as they come to my mind again.
Your assumption is absolutely correct!
Of course you can also use something like