The sentence 'Let me know if you need any help' is correct and usable in written English. You can use this sentence to politely offer assistance to someone. For example: I know you're busy with the project, so let me know if you need any help.
"Let me know if you need any help or introductions.
Let me know if you need any help finding good resources.
Let me know if you need any help, I'm available.
"Let me know if you need any more stuff".
Take care of it, and let me know if you need help".
Let me know if you need help.
It might be natural to offer to help by saying, "Let me know if you need anything at all".
"Let me know if you need anything".
Let me know if you need more information.
"Please let me know if you need anything else".
Let me know if you need my ear".
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union