I'll asume that if you clicked on the 'keep reading' button, you've read the book The invisible life of Addie Larue and won't be bothered by spoilers. So here we go: my opinion on wether or not Luc loves Addie *sorry if it's too chaotic, my mind's all over the place again lately*
At some point in the story, Luc and Addie fall in love. Of course they did. They're both basically imortal, he's the only one who remembers her, she's the only one who keeps him company. They talk, they fight, they get to know each other, they bond, they fall in love. Simple as that, right? Well...
Few pages later, Addie suddenly doubts Luc's love for her. She thinks he fakes it to get her to give up her soul. And despite the narrative implying that that's not Luc's intention at all, he only protests meekly.
Now is where opinions gets shared: is there truly more to Luc's story or is Addie right? We know nothing about him. He's sarcastic, inteligent, handsome and powerful. He is like the needed evil in fairytales so the hero/ine can grow and learn and reach the true potential. Not knowing his backstory is hard to sympathize with him. Hard to see him as something more than what Addie sees him as: one eons old bastard whose only drive is collecting souls (why exactly? we don't know).
Therefore, it is hard to think that he genuinly falls in love and doesn't just wait for her to lower her guard. Addie isn't overreacting or jumping to conclusions. She is right to assume.
But the question of Luc's feelings comes even later, when he offers Addie a new deal: herself for Henry's life. Why would he give up the chance to get her soul if that is what he really, really wants? Why accept to lose a soul that's basically already his and can't escape him, Henry's, for the chance to have Addie with him for eternity? Once Henry dies, Addie might be broken enough to finally give in, offering him both of his payments. And even if she'd be motivated by grief and hatred to keep living to spite him, Luc would still be in gain. So why that last deal? It's not something any smart, experienced, eons old villainous god would do. Which is exactly what Luc is. So the answer must be he wanted her more.
However, I don't think it's love. Love isn't selfish or cruel. Love would have pushed him to persuade her before meeting Henry. Try to explain, try to prove himself, show her he's trustworthy. If it was love, Luc would be shown to grafually become more humane. We'd get a reason for why he's doing what he's doing, we'd be allowed to see more of him, understand him, pitty him even. Or the opposite. But he'd be more of a presence than only showing up to rile Addie up, help her achieve her true potential and give us delightful scenes.
In conclusion, I don't think Luc loves Addie. Seeing how little we know of him, he seems to not know what love looks like. He starts to admire her, crave her. And he calls that love. He wants her, he's possesive of her and slighlty jealous, leading to him being eager to accept a deal that's not advatageos for him. But he doesn't love her...
... yet (I still think there's potential for them after the ending, but I know there won't be a second book, so yk, daydreaming).