[efdee]

"Let us go" does not only mean "you should let us go" but it is also the first person plural imperative implying that we go. Whether you shorten it to "let's go" or not does not change this.

Same as how "let us pray" is frequently used as well.

[esafak]

Abbreviation does change it; it narrows the meaning. "Let's go" never means "you should let us go" and "let's pray" never means "you should let us pray".

@ninkendo shared an insightful video below about it. https://en.wikipedia.org/wiki/Clitic

[efdee]

Nowhere does anyone claim that "let's go" means "you should let us go". The discussion was whether "let us go" automatically means "you should let us go", which it does not.