Visible crew/equipment: During the doctor's office scene, when Larry walks over to pull the paper across the bed you see beige directors tape on the white rug in a distinct "T" shape instructing Clive Owen (Larry) where to walk.
Visible crew/equipment: At the end of the film, when Natalie Portman stops at customs, look at the bottom left of the screen when she hands over her passport. The bottom half of the camera equipment is reflected in the glass. (01:36:40)
Answer: It appears so. Nothing else suggested he knew where she worked. More that he was just going to different clubs and drinking and came across the club Alice was working at.
Lummie ★
I think he knew exactly where to find her. He's a doctor and often doctors are known to have that "God" complex. I think he wanted to gain control of his relationship with Anna. To win Anna back he had to manipulate all the players including Alice/ Jane. He probably researched her and found her. That's why he knew Alice/Jane was not her real name. He was low key stalking all of them, to get Anna back.
At the strip club, Larry does *not* know that her name is legally Jane. He thinks her name is Alice. She is using a stage name at the club, and he wants to hear her say that her name is Alice. He refuses to accept "Jane" as the answer. He is waiting to hear "Alice."
But Jane actually was Alice's legal name. This is shown at the end of the movie, on her ID. Larry did not believe her when she told him.