Yes, you get gold reward for all other levels.
And I've done gladiator promotion quest, Although I don't have any gladiator in my team, just done it work experience and gold.
The problem with Lord level is that after I kill all the guys and report back to the Arena NPC dialogue script seems to break, I tell him I've won, he congratulates me, at this point I should get gold reward and have other dialogue options to fight again/watch fight/put a bet. There are not there and We've won option is still there.
If I leave Arena and return the dialogue options are back, We won is still there and wont do anything at this point. I can again go fight, picking different difficulty level and get reward as long as it wont be Lord level.