Can Baron Nashor leave the Baron Pit?

Yes, Baron Nashor can leave the Baron Pit.

While Baron Nashor's ability requires him to enter the Baron Pit when he is played, there is no rule or card text that restricts him to that location once he is already on the board. He functions like any other unit and can move to other battlefields or his base if an effect or action allows it.

Additionally, note that the Baron Pit itself has the ability: "Units can move here from anywhere." This ability facilitates movement to the Baron Pit, but it does not restrict units currently at the Baron Pit from leaving it.