No, the two are different. "Let her go" is a suggestion/advice given to him only. Also, the sentence is a complete sentence that uses the imperative mood. "Let each other go" would be advice to BOTH (not just him, as it is in the first). As well, this is a sentence fragment and not a complete sentence. To give the advice to both, you would have to say something like "Both of you should let each other go". Edit: I misread your question a little, but I think I've managed to still answer it :)

Yeah that's correct

Hello 🥰! Let her go means that you are reffering to person A to let go person B. Second part means that you are referring to both persons A and B and that you are suggesting them to separate. 😃