Let’s + infinitive without to is often used to make suggestions. It is rather like a first-person plural imperative.
- Let’s have a drink. ( = I think we should have a drink.)
Let’s go home, shall we?
There are two possible negatives, with Let’s not . . . and Don’t let’s . . .
- Let’s not get angry. Don’t let’s get angry.
Let’s not is considered more ‘correct’.