Another Duo user offered the following useful explanation for a different sentence with a similar construction: When "lasciare" is followed by an infinitive or a subordinate clause it means "to let" or "to allow"; when it is followed by "per" it means "to leave sb to do something".
True story: I was visiting a friend in London many years ago, when he was living with his parents just after College graduation. Mom and Dad had some strange notions about food, and the meals they served were skimpy and made of God-knows-what, with a taste not fit for the worst restaurant in the world.
Except for the dog. The dog was served freshly cooked hamburger. My friend and I were considering stealing the dog's food, but we went out to a pub instead for some fish and chips and lots of beer. (I happened to really like the warm beers they served there, which is weird for an American.)