A thought experiment on Luka's form of love, Hyuna, and Hyun Woo.
Purple Rose -> Anxious Love
"He instinctively knows that his love is insecure."
Anxious love / insecure love -> Love is insecure, unstable, and like all emotions, malleable. It's subject to change. It is not everlasting. It can grow, it can dwindle. It is impermanent. Whether it be his own feelings, or other people's feelings for him.
Luka, who is self-destructive yet at the same time hurts others, with his pure childish yet seemingly inherently evil nature, could not be accepted with beauty alone.
— Artbook, Luka's Profile
"If you're born and raised in a restrictive environment where every breath you take, every facial expression, every angle of your mouth is controlled, you don't even have a chance to think about 'healthy love'. But love is still love, and it's not like Luka didn't try."
Unhealthy love -> His methods of loving are not conventional or healthy; he does not hold the same concept and understanding of love as we do, that some like Hyuna and Mizi are lucky to.
Luka is the product of his exceedingly twisted environment — more than the others due to the nature of how controlling it is. He isn't allowed to exist outside of what that environment demands him to be. Nevermind a toe out of line, "every angle of your mouth is controlled."
All this ties into the flashback sequence from All-In in an interesting way.
He tried to come onto Hyuna due to his feelings; the wrong approach stemming from his skewed and lacking understanding of love.
The rejection from Hyuna reminds him once again that love is not guarenteed and that love is not stable.
Due to this blow, he turns towards a different method to securing their relationship— blood.
"Luka thought the whole time he was away from Hyuna. About what he should have done, and how on earth he could be more connected to his loved ones than blood."
By killing Hyun Woo, Luka has essentially tied himself to Hyuna through a "bond of blood."
Even if Hyuna will never develop feelings for him. Even if one day his own feelings change, they will always be tied through Hyun Woo.
Luka's expression, which is a big part of Hyuna's trauma, is smiling as if he feels joy even though he is covered in blood.
Control -> he cannot tether himself to his loved ones through something as insecure as feelings. Thus he uses blood instead.
No matter what state it's in or what form it now takes, his bond with Hyuna has been been eternalized. Even after so many years, it remains tethered and strong.
Hyuna's inability to leave her trauma behind, her inability to leave him behind, has given him a joy no one else can understand.
Even if her heart wavers due to betrayal or unrequited affection, she still chooses the path of love.
— Artbook, Hyuna's Profile
"Unrequited affection" -> either referring to her inability to return Luka's feelings thus leading to the incident, or referring to Luka, repaying her and Hyun Woo's care with murder, thereby not reciprocating their affection for him in the same form he received.
"Betrayal" "I never should have been nice from the very beginning" -> Because she was affectionate to Luka, he developed feelings for her. Because she could not return those feelings, he attempted to form a different bond, one tied in blood. And in the end, she lost the one most dear to her in this world, her "one and only jewel." She sees accepting Luka as the greatest mistake of her life.
This one I'm not so confident about but it's a possibility that gives food for thought.
"Be more connected to his loved ones than blood" -> he has attempted to connect to a loved one through blood previously
"Loved ones" -> Hyuna isn't the only one he loved (ofc this could be a generalized term)
During his Anakt days, his beauty stimulated the curiosity of the other kids, but after they came to know his true self, they could never become friends with him.
— Artbook, Luka's Profile
There's no mention of him in Luka's materials despite Hyun Woo playing a huge part in his life — the first person to accept him, the catalyst for his bond with Hyuna, the catalyst for the break down of his relationship with Hyuna.
Either Hyun Woo doesn't even make a bleep on his radar, or it's because he matters (... or mattered) that Luka refuses to touch on the topic of him.
The bond he attempted to forge through Hyun Woo's death might not be just about Hyuna, but Hyun Woo too.
Hyuna's rejection emphasized Luka's insecurity and inability to believe in the longevity of their relationships.
Thus Luka killed Hyun Woo, while the latter still cares about him.
He already failed with Hyuna. But this one, with Hyun Woo it's not too late yet. Before Luka inevitably destroys his relationship with him, he should kill him, so that eventuality can never come to pass.