Answer:
The air is very stale in the library; moreover, the lighting is poor. (second option)
Step-by-step explanation:
A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.
Only the second option has a semicolon linking two correctly written independent clauses.
When the conjunctive adverb moreover introduces a new independent clause in a sentence, use a semicolon before and a comma after this conjunctive adverb.