Oooo... That's a good one. At first, it would seem that Satan is the stronger of the two, especially with the "Far Higher" key, there were two problems with that. For one, I wasn't able to find any calcs or scaling for Satan besides ManBearPig>Satan>PC Principal. Two, Satan had been turned submissive through abuse from a dictator of all things.
Lucifer, on the other hand, had something to scale from: the Helltaker, who was capable of 0.023 tons of TNT. That's not to mention that Lucifer is far more likely to take control than Satan. In the expansion for Helltaker, she outright told #67 that she planned to take control back from Azazel (Loremaster at the time). Sure, you can tempt Lucifer with pancakes, but that's not really a weakness, it's more of a "Meh. I'm bored. I'm gonna go suck this guy's dick for some pancakes."
Lucifer has a kiss of death, which may not seem effective at first thanks to Satan's Type 4, but when you consider where Satan respawns, depending on where in Hell Satan respawns, he might not have a clue where Lucifer is, potentially giving Lucifer a win by BFR. Of course neither the Bible nor Dante's writings had a clue whether Hell is finite or not, so I can't exactly say whether there's a monkey wrench being thrown in there or not. What could be a monkey wrench, however, is whether the Hell Satan spawns in would be his version or Lucifer's version. I say that because if he respawns in Lucifer's version, more than likely he'll be caught in a death loop since abuse victims are very unlikely to have the necessary willpower to deal with Lucifer's version of Hell.
I think I'll give it to Lucifer, it seems more likely Lucy would win than Satan based on what I could tell.
