While you were in the lobby, did you notice the piece of paper on the check-in desk in the middle of the room?
It says, among other things, "I left the key. Check the stairs." So there is a key around somewhere. We need to "check the stairs," so go out the door to the right, which leads to the only part of the building where you can actually see stairs.
But it's not the stairs we're interested in. The right wall of the room with stairs is covered with graffiti. Look at it closely to see that one of the words is underlined. (In my game, the word was "Rebuke," but it might be another word for you, so just remember the word.) Have you seen similar words anywhere else in the area?
Switch back to Rosa and look at the bricks to the right of the door. Sure enough, it's the same words as in the inside graffiti. And if you click on the word that was underlined inside, Rosa says the brick is hollow but the ice is sealing it shut.
You don't have a cigarette lighter in your inventory -- remember, it was Rosa's aunt Lauren who was the smoker -- but you do have something hot that will melt the ice.
Use the coffee on the brick and pull out the brick to find the key.