Lerma went down clutching his face following an off-the-ball incident in the first half of Palace’s 2-0 win.
Anderson escaped punishment despite a VAR check and Bournemouth manager Gary O’Neil has said he will speak to PGMOL chief Howard Webb.
O’Neil feels there should have been further action taken against Andersen.
O’Neil said: “Jefferson has broken his nose. It looked like a punch in the face from the footage I saw.
“It looks like a punch so I would expect VAR to step in. Jefferson is in a lot of pain, and is obviously disappointed he has broken his nose. It should probably be looked at.
“I am not sure what the punishment should be but a punch in the face is a fairly serious offence.”
Palace manager Roy Hodgson said: “I have no idea what happened or how the player landed on the ground but I have to trust the referee, who did not see any reason to give a free-kick. That was backed up by VAR so that was perfectly good enough for me.”
Palace won the match 2-0 with two goals from Eberechi Eze.