What is the correct translation of "let's meet up"?
Lass uns uns treffen
Lass uns treffen
is correct. As Hauser pointed out, it is not good style, though.
You can easily see, that it is correct if you replace the Akkusativ object:
You cannot omit the Akkusativ object, so you cannot drop the second "uns".
In this case (for the "better" style) I would use:
(See your other question for details ;)
I don't like the doubled uns (matter of personal style), I would rather use a rhetorical question
It matches -imho- the meaning of "Lasst uns" in colloquial German, which basically is a question/request, as the other persons still have to agree with your suggestion.
Would be a real question and request to discuss the point of a meeting.
is the correct one. "Lass uns" ist the correct (albeit literal) translation of "let's", "sich treffen" is reflexive and needs the reflexive pronoun. If that becomes "uns" for grammatical reasons as it happens here, and meets the "uns" in "Lass uns", then you need both instances of "uns".
In reality you will probably also hear "Lass uns treffen", but this version is grammatically incorrect.
edit: As bernd_k points out, when you are addressing several people, you indeed need to use the imperative plural, "lasst".
I think it is correct, when you address a single other person. In case you address a group of people, better to say:
"Lass uns einander treffen" is both correct and good style (though might be viewed as overly sublime in day-to-day spoken language).
"Lass uns uns treffen" is correct, but obviously not very good style.
"Lass uns treffen" is often used informally, even though it is formally incorrect.
EDIT: I'd like to point out that the "Lass uns..." wording is also a bit colloquial.