I think the Percy Jackson show is going for Luke being redeemable at the end, and I personally don't think that's right.
Here's the thing. Luke is redeemed (specific wording here) at the end of the series. He is given motive for his actions and a final good deed, followed by a hero's death. He is, by narrative definition, redeemed.
However, I think the really important part of that is that he still did everything. He still voluntarily chose his actions, knowing what they would result in. He wasnt tricked, or manipulated (not fully) or controlled. His actions were of his own free will, both the bad and the good. His reasons don't make what he did okay, nor does it make them not his fault.
I think thats why Luke is such an interesting antagonist, because I don't think we're supposed to agree on whether he's a good guy in the end or not! That his final actions and his motives redeemed him fully, or that they weren't enough to balance out the harm he caused, both are completely valid viewpoints, both held by people in the books because it's just not that straightforward.
Which is what I don't like about the series rn - they're making him too good. He's putting Annabeth and Thalia above his goals, he's hesitating, he's got Kronos in his head causing him pain when he disobeys - all of these things, I reckon, are them setting it up for him to be fully a hero by the end, which he shouldn't be. They're making him good to justify how Annabeth still cares about him, and how they'll call him a hero after he dies - but the whole point of Luke is that juxtaposition! That despite all of his evil deeds, he simultaneously dies a hero. He's both at the same time, because life is so much more complicated than heroes and villains, something that Greek Mythology in particular likes to show us (cough Achilles cough Odysseus cough).
The whole thing is nuanced, and you might read this and think "No, Luke was a [hero/villain]!" But thats the point, that both viewpoints should exist simultaneously and equally validly. He is both and neither and that's what really hurts Percy and Annabeth and those who knew him, and that's what (in my opinion) makes him a great antagonist.