In a lot of the stuff I've read, arcane lineage is treated like a get-out-of-jail-free card for character development, which honestly kind of grates on me. It's supposed to be this huge burden or secret power, but too often it just means the necromancer gets to be special from page one without having to earn it. I prefer stories where the lineage is a curse first, a power second. Like, maybe the magic in their blood makes them sick, or attracts ghosts that torment them, or marks them for persecution. That forces a different kind of growth—not just learning bigger spells, but learning to live with this thing that's as much a part of them as their own bones.
Take Sebastian de León from the 'Magebreaker' series. His family's pact with a death god isn't a cool party trick; it's a debt that comes due every generation. His entire arc is about trying to break the cycle, not master it, and that struggle against his own bloodline is way more interesting than another Chosen One narrative. It gets into questions of free will versus destiny, which is fertile ground for a necromancer character. The power isn't the point; the choice of what to do with it, or whether to even use it at all, is.
Ultimately, I think the best use of arcane lineage is to create internal conflict, not external advantage. It should complicate their relationships, limit their options in some ways while opening others, and make their victories feel bittersweet. If their growth is just about leveling up their inherited magic, I lose interest pretty fast. But if it's about them figuring out who they are separate from that lineage, or how to redefine what it means, that's a story I'll stick with.