Answering with "Let's!" or "Let's go!"

I have been reading conversations like the following:

Person 1: Hey, let's go for a jog this afternoon!
Person 2: Let's!

Is it correct to only say "Let's!" instead of "Let's go!"?

Solution 1:

Yes.

Answers to questions often omit words which would be repeated from the question:

“Did you do the dishes?” “Yes, I did [do the dishes].”

The response “Let’s!” is a grammatically quite standard example of this, and it can mean other things beside “Let’s go”:

“Do you want to see a film tonight?” “Yes, let’s [see a film tonight].”

Depending on where you live and whom you talk to, though, “Let’s!” on its own may be more or less idiomatic than “Let’s go!” or other similar answers. To my ear, “Let’s!” alone seems a bit unusually curt; but “Yes, let’s!” or “Do let’s.” are both quite normal (the latter being perhaps more old-fashioned and more BrE).

Solution 2:

It's a common enough expression, but more likely, I'd have thought, to occur as Yeh, let's.

Solution 3:

Let's being a contraction for let us, responding "Let's!" to the suggestion to jog is properly informal and conversational.

(Responding with "Let us!" sounds like you're asking permission.)

There's nothing wrong with answering "Let's go!" but it's not necessary, unless Person 2 perhaps wishes to imply "Right now!"