Is this the correct use of the word 'lieu' in this sentence.

The store let me trade the item for something else I liked in lieu of returning the money.
?

A synonym for the word lieu would be place as well.

Yes. That's a good sentence.

Yes, the use of the word 'lieu' in the sentence you provided is correct. 'Lieu' is used to mean "instead of" or "in place of." In this sentence, it is saying that the store allowed you to trade the item you purchased for another item that you liked, rather than giving you a refund or returning the money to you. It indicates a substitution or an alternative.