Learn English – Do you know or did you know

The second sentence is definitely the correct one:

If I change my mind, I'll let you know.

You or your friends are probably confused because when "I'll let" is spoken, all those "L"s blend together and sound like "I let". Don't be fooled by that.

Try the same tense with different words. Which sound correct to you?

Incorrect: If I change my mind, I buy the product.
Correct: If I change my mind, I'll buy the product.
__

Incorrect: If I win a lottery, I donate the money.
Correct: If I win a lottery, I'll donate the money.

The copyeditor in me observes that your at there adds nothing to the sentence: leave it out.

It’s also something of a shibboleth whose use will mark you as “poorly educated”, because these things are expected to have been corrected in the course of proper schooling. The same is true with questions like “Where are you at?” Here again that at at the end adds nothing — or at least, nothing good — and should be omitted.

Once upon a time, surely aeons ago now, there was something of a hipster phrase about “where it’s at”, referring to some location or event or even style that was supposed to be “really happening”. Unless you’re trying to faithfully recreate the special slang from that period in history, I would avoid it.