Coming late, which is shameful because I'm huge fan of Lucifer and it's one of my favorite series
In general, there stuff I agree with and others I don't.
- Sound Manipulation: I agree, cause his voice clearly has a reverb effect and everyone can hear it, not simply Chloe.
- Pain Manipulation: I agree
- Hellfire Manipulation: As much as I would him to have that, I don't think we can afford it. He doesn't demonstrate it as an ability in his series and the depiction of Hell in the series doesn't involve fire.
- Invulnerability: I would change it to Nigh-Invulnerability, cause he can still be harmed by supernatural creatures and weapons, his invulnerability "only" plays out for mortal weapons and normal humans so it's mostly partial.
- Enhanced Senses: Disagree for that example. He realized he was vulnerable because he hurt himself on the stairs, he looks clearly surprised when he sees Chloe coming. HOWEVER, I would say Enhanced Senses can be warranted by angels hearing prayers.
- Clairvoyance: Agreed.
- Reality Warping: Agreed. It's even a major plot point in the last season, angels are lost without a ruler for Heaven so they start granting prayers and accidentally cause mayhem, I remember they even bring a lion to life due to one prayer so he definitely should have that.
- Cosmic Awareness: I agree. He apparently didn't leave his Earth yet was aware the Multiverse was ending.
- Power Bestowal: Disagreed. It's an entirely unvoluntary effect based on self-actualization, Power Bestowal is something that must be wanted.
- Power Nullification: Same as above, Power Nullification is about voluntarily nullifying an ability.
- Teleportation: I...don't know. He seems capable of appearing randomely at will like distance doesn't matter even in Season 1 when he doesn't have his wings, meaning it's not like the other angels who can fly so...I don't disagree with it in essence, I'm just not sure.
- Possession: I'll speak about it later but I disagree with this one. Angels in the Lucifer series are never seen possessing a human.
- Magic: Don't really see any reason why he shouldn't have this but he never demonstrates proper "Magic", all his powers are inherently angelic. I didn't memorize every line so I can't exactly remember but I do believe sorcery is mentionned. Still not sure though.
- Self-Sustenance: Agreed for Type 2, disagreed for Type 3 and for Type 1. We see him tired several times in the series, even when he's not vulnerable due to Chloe and we see angels breath to (Michael is clearly breathing in the four-way battle in 5X08). On the other hand, I can't remember a single time where he complains about being thirsty or hungry.
- Ice Manipulation: Agreed, the mention about freezing Hell is pretty clear, especially since we see him shaping it however he wants it to be in Season 5.
About Hell, I think Lucifer should get a key for it. He doesn't have many abilities related to Hell on his profile but he already has many and adding more would make the page heavy. Plus, ice would only apply for Hell and same for Hellfire if it gets accepted so we can still gather them under the same tabber to make it more clear. Btw, his current Hell tier is "
4-C in Hell" but while putting him to
Low 2-C is a big jump (logically, Hell in Lucifer would be infinite since it's been there since the birth of the Universe and is supposed to imprison the souls of all evil humans who have died ever since Cain and Abel some billions of years ago and even other beings ever since its creation, I think it's safe it has to be nigh-infinite or something similar to house all these souls but there's no clear statement about that unfortunately anyway), I think we can safely change it to "at least
4-C in Hell", since he should be able to do much more than creating a sun.
Now, about the Arrowverse connections, the two series exist in the same Multiverse. Satan from Earth-1 is not Lucifer's counterpart like stated on the Arrowverse wiki (if we don't use the wiki to upgrade the character, I don't see why we should use it for a downgrade), they're clearly two different characters. For example, Satan has bat wings and a different powerset and personnality, so it's not a case of alternate counterparts. God creating an alternate Lucifer in Once Upon a Time is not related to Satan at all and doesn't mean Lucifer has multiple alternate versions.
However, there are indeed two different Hell. Hell in the Arrowverse is depicted as a giant, Balde-Runner-like city (minus the neons) while in Lucifer, Hell takes the form of a dark and ash-filled endless maze of doors with the damned locked behind them. Note that it's the exact same Hell during the whole series and while it's implied Lucifer can change it however he wants as its ruler and in the Arrowverse, there's no mention of anything related to Lucifer each time Hell has been shown (you can say he left long ago but the fact remains the two Hell have a different appearence anyway so the two realms are definitely different).
The confusing stuff is that Lucifer clearly exists in the Arrowverse but we only see him interacting with his own world aside from Constantine, Mia and Diggle on-screen, even though (again) he's clearly part of the greater Multiverse. While I would love a big upgrade for him, unfortunately we can't afford one (especially since now both the Arrowverse and Lucifer are over). So stuff related to the Arrowverse like possession and Magic are doubtful.