Should I use "Let's" not "Let me" in this situation? I thought "let me" sounds more natural.
"Let's" in this context is used to introduce a suggestion, request, or tell someone what is going to happen. This is a common use of "let's" in English. "Let me" could also be used in this particular scene. Ex: A: What should we do this weekend? B: Let's go to the mall. Ex: Let's forget about what happened, okay? Ex: Let's get you some medicine, you need it to feel better.