How do you get inside this area at Washburne Refinery?
In this area there is a door with a lever and behind it seems to be some sort of arena. During my normal first playthrough, this door was locked and the lever unfunctional.
How do you get inside and what is there to do?
This arena is where Hyperius the Invincible stands around all day waiting for challengers. You will receieve a quest for this boss after beating all the story missions in the Scarlett DLC.
He's level 50+ and it's a very hard fight, for some tips on how to beat it check out this question.