- let us (more formal)
- Used to form the cohortative of verbs, equivalent of the first-person plural imperative in some other languages.
- Let’s eat lunch sometime.
- I say let’s dance.
- Used to form the hortative of verbs, equivalent of the second-person plural imperative in some other languages, chiefly instructional
- Let’s make sure we don't forget proper punctuation.
- Hey guys, let’s check to make sure that we proofread.
- Y'all, let’s stop talking please, y'all are driving me up the wall!
Let’s always includes the addressee(s) and usually (but not always) the speaker, while let us commonly refers to the speaker and others but not the addressee(s), especially in a modern context.
- Let’s go, we are late. (inclusive we)
- Release us and let us go! (exclusive we)
Negation of let's is let's not in standard English.
- Let’s not talk about it.
Don't is also used, but it is often considered non-standard.
- Let’s don’t talk about it. (US)
- Don’t let’s talk about it. (British)
Tag questions with let's typically take shall we?.
- Let's go to the beach, shall we?
- American English and British English, Concise Oxford Companion to the English Language, Tom McArthur, 1998.