Which one is correct or are both correct? Please explain if there's any explanation.
Let's do kiss
They're both correct, there is a difference in meaning.
Do X where X is the plain form of the verb is required for:
A reason for do X emphasis is to make it clear you want to do X as opposed to something else - and you were considering it earlier.
The usual situation (and implication created) is there was some indecisiveness or unclearness on what happened and then you made a decision on what to do.
So what happened? Did you walk or run?
Well, we wanted to walk, but it was better to run because of the dog. So we did run (as opposed to walking).
Another contrived example of present tense usage:
We need to go to work soon.
I want some coffee. Weren't you thinking of getting some earlier?
Yeah, that's a good idea! Let's do get coffee.
If there's any doubt, don't use the do.