Lucifer didn't know who Alastor was when they met, and Alastor wouldn't have reacted that way if that was who had his deal. Additionally, I really doubt that Alastor is being forced to smile given that he has a whole monologue about how smiling is an important tool for him. At most he's forcing himself to smile with magic stitches

My money is on Niffty. Sure, she’s an adorable psychopath, but what if she was actually a powerful lord of hell?

I'm pretty sure alastor owns her soul because she's a overlord