Note this is strictly Lucifer from the video game Dante's Inferno. The OVA is very obviously not canon. The short Comic Book Series on the other....very well might be canon, it's really close to the game including like shot for shot recreations. Not a lot there regardless but I will note when something comes from the comics specifically.
Lucifer was once the greatest of God's Angels but God made mankind in his image. Lucifer, appalled at the "flawed creation" refused to bow before them and attempted to betray God and so was bound at the bottom of Hell. Lucifer enacts a scheme to manipulate Dante the crusader, the darkest soul in human history into freeing him.
Lucifer is incredibly strong. He was bound with the Chains of Judecca that circle each of the 9 Rings of the Inferno, each ring being large enough to contain mountain sized giants and having their own separate horizon. However even this seems weaker then his true form which he described as going to "make the Earth tremble, shake kingdoms, and leave the World a Desert" suggesting Multi-Continent Level to Planetoid Level Strength. His durability of a similar level as he can engage in physical combat with Dante, his physical equal.
Lucifer in his true form should be comparable to the Angel that came from outside of Hell to the bottom of the 8th circle, second lowest, in seconds to reclaim Beatrice, a feat that would likely take at least triple digit mach speed, likely 4 digit mach speed. Indeed in mid-combat within a few seconds of being released into his true form, Lucifer almost escapes Hell just by flying despite the size of Hell.
Lucifer also claims to be a threat to the universe saying he will "plunge the cosmos into chaos" and that his awakening meant "the end of the universe", however they are vague statements and could be taken to mean a lot of different things. However it might imply that he could be a gradual universal threat by an unknown method.
Where Lucifer really shines though are his abilities. Lucifer is immortal in the ageless sense but also has a greater degree of immortality. Despite being impaled by Death's scythe, he was unaffected and actually caused the scythe to disintegrate from sheer force of will. Related to this he regenerated the wound caused by the scythe almost instantly.
As might be expected Lucifer can fly, in his true form and likely in his Giant Form if he was ever unbound. Even trapped in Hell, Lucifer can astral project himself, his astral projection able to teleport even to the surface at will and turn into darkness. He also remotely teleports hellish pomegranate seeds to himself to feed to Beatrice.
Lucifer is a clever manipulator and this is bolstered by his psychic ability. He can see distant events with Clairvoyance and show them to others. The Comics imply that he is telepathic and that he controls all the sinful of Earth. It's also sort of implied that the Damned do what he tells them to, although that might just be psychological trickery. Lucifer can also take souls though he has to win a bargain against a person first, which means it is likely unusable in combat unless he's fighting a particularly arrogant character.
Lucifer also has black magic giving him control of fire, wind and ice as well as dark energy blasts and forcefields that protect against holy magic. He can remotely give dark magic to his worshippers. It's also implied in the comics he opened a hole from Earth into Hell. He also shapeshifted into a snake.
So, how would he do in other verses:
In the DC Comics universe, Lucifer would require one of the verse's "flying bricks" to defeat due to his massive physical stats and even low levels of their kind could potentially be defeated by his array of tricks. Most Flying Bricks due have the ability to incapacitate him, though it would take one of the verse's more hax members to actually kill him due to his immortality. The vast number of supervillains means if he really can control the sinful that he would become a massively larger threat.
In Marvel Comics, Lucifer would be roughly equivalent to an Alpha Level Mutant, though with the versatility of an Omega Level Mutant, or a High Meta Tier Methuman though more dangerous then most. Similar to DC the massive amount of supervillains could theoretically drastically increase his threat level fast.
In the HST, while Lucifer would not be the strongest character in any stat, he would be very high up there and would be extremely dangerous threat to all known civilization with his vast degree of haxes. He very likely could solo One Piece, though Bleach's relative inaccessibility to him and Naruto's god tiers raw tiers may allow them to stop him.
In the Bastard!! universe, Lucifer would have weaker stats and haxes then any True Form Demon but his manipulation and general versatility would allow him to be about on par with low ranking Demons like Anthrax. Much like Anthrax, especially given his ability to grant dark magical powers, it's likely he would get a cabal of worshippers on Earth though if he tried to defeat the Earth, even back before the 4 year time skip, Dark Schenider would likely be able to defeat and most likely even kill him with much less difficulty then the fight with Anthrax due to his lack of passive defensive haxes.
In the Dungeons and Dragons universe, Lucifer would automatically be stronger then almost any Demon or Devil in the verse, and would likely end up an Archdevil Rank, having more power then most (about comparable to Mephistopheles the second strongest Archdevil), but not being as versatile or hax then Dungeons and Dragons magic. However because he would very quickly gain a following on Earth due to his passive pseudo-planetary control he could theoretically grow in power fast. However while his manipulation ability is great he wouldn't be able to out manipulate Asmodeus, the strongest Archdevil and would get crushed in a battle against any Deity level entity.
In the Darkstalkers verse, Lucifer would hold an...interesting...position. He would be far below the actual cosmics of the verse in terms of power, but would be well above everyone else in the verse, due to his comparable speed, greater physical ability, bordering on cosmic, and his high versatility and hax comparable to greater to the verse's non-cosmics. While he could theoretically manipulate some of the hotter headed members of the Darkstalkers Cosmics psychologically, he would get destroyed in any kind of direct confrontation though if none of them got involved it's likely he would have complete dominion over the Earth.
