the use of let's

Would it be correct to use an apostraphy s in this sentence and why?

She let's me go boating.

[mykwyner]

The apostrophe is an error in that sentence.

Lets is the third-person present of the verb [to] let meaning allow or permit.

Let's is a contraction of let us.

If my mother lets (allows) me go, we should go today.

I'm busy today, let's (let us) go tomorrow.

[Casiopea]

Weclome.

Correction
Would it be correct to use an apostrophe . . . ?

All the best,