Does “Let me know if you have any questions.” mean “reply only if you have a question”?

Does "Let me know if you have any questions" mean that there is no need to reply unless you have a question?

I get informational emails sometimes that end with some form of "Let me know if you have any questions" or "Let me know with any questions", for this specific instance it's my landlord telling me about scheduled maintenance of the elevators.

Should I reply with a short thank you or should I not reply anything unless I have a question?

As a matter of the English Language, "let me know if ..." has no implication of requiring a response if the conditional is not met.

As a matter of etiquette, it does not matter if you reply or not, and would usually depend on context.

In a company with 2000 people, I am sure the sender of the email would not be happy to get flooded with 1995 "thank you" responses and have trouble finding the 5 people who need additional information from them.

In a scenario like you described where the landlord sent an email to a handful of people, it would be okay either way. It's more polite to reply "thank you", but some people might see that as overdoing it, and certainly no one would think any less of you for not responding "thank you" to a mass email.