Who's means who is or who has. Whose shows possession. The apostrophe is the whole test. Word-choice questions like this sit with diction on ACT English.
Swap in the long form
If who is or who has fits, use who's. Who's leading the lab? means who is leading. If you are talking about something that belongs to someone, use whose. Whose calculator is on the desk? There is no “who is” hiding in that sentence.
Whose can refer to things, not only people. The school whose roof leaked closed the gym. That is possession, so the spelling without an apostrophe is right.
The apostrophe is doing contraction work
Same family as your versus you're. The mark stands in for a missing letter. Possession rules for nouns are in apostrophes on the ACT, and the broader grammar list is in ACT grammar rules.
The bottom line
Expand it. If you can say “who is,” use the apostrophe. If something belongs to someone, use whose.
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