When I load up an engine (like Stockfish), it reaches a higher depth quicker if I only leave one line of analysis open. If I leave multiple lines open, it runs slower. Why is this?
That's normal, commonly known as multiPV analysis.
Without getting into too much technical details, analysing N number of principal variations require running the engine N times, one for each PV. We need to do that so we can estimate a precise score for each PV.
With only one line of analysis open, engines are able to prune the other sub-par lines (since you don't want to know anything about them). By leaving multiple lines of analysis open, the engine must fully evaluate each of them, and can't prune any of them (even if they're guaranteed to be worse than the best line showed at the #1 spot).