Usage note:

Let us is used in all varieties of speech and writing to introduce a suggestion or a request:

Let us consider all the facts before deciding.

The contracted form let’s occurs mostly in informal speech and writing:

Let’s go. Let’s not think about that right now.

Perhaps because let’s has come to be felt as a word in its own right rather than as the contraction of let us, it is often followed in informal speech and writing by redundant or appositional pronouns:

Let’s us plan a picnic. Let’s you and I (or me) get together tomorrow.

Both Let’s you and me and Let’s you and I occur in the relaxed speech of educated speakers.

The former conforms to the traditional rules of grammar; the latter, nonetheless, occurs more frequently.