I wouldn't let them do it, not if they don't pay you
are the meaning the same in above sentence with or without 'not'?
My first understand to this sentence is that the whole sentence should be***'I wouldn't let them do it and I would not let them do it if they don't pay you.'***
My second understanding is 'not if' here means 'unless', but I didn't find any definition of 'not if'.
Not is acting as an emphatic. It means that the speaker wouldn't let them do it if they didn't pay the person they are speaking to. It is particularly strongly emphasising that that is a strong reason not to let them.
Your first understanding is correct.
The speaker is apparently thinking as he is talking.
His first statement is, "I wouldn't let them do it," which is clear enough.
But, he goes on to make another statement which is not exactly the same as the first one, namely, "[I would] not [let them], if they don't pay you."
According to pure logic, it is left unspoken whether you should let them do it if they do pay you. But since that possibility is not addressed, we are left with the impression that their paying you is out of the question. It sounds like it is obvious that they will refuse to pay.
So we are left with a simple clear statement followed by an if-statement which sounds like it could involve a possible contradiction to the initial statement (if they do decide to pay you). But in this case I think it is assumed that the "if" condition won't happen (they would never pay you), so the second half of the sentence is really an explanation of why the speaker has said the first half.
I think what the speaker means is, "I wouldn't let them do it, especially since they aren't going to pay you."
