Okay does Lydia have specific requests (His archangel name list is kinda of limited but they can try figure out). Henry advises she should get his own type of hallowed vow and try use it to improve her own senses.

"Senses could be useful, I'm a bit behind all the werepeople. Do you think that would negatively affect my banshee abilities?"

"I think if it is either going to improve your special senses or fail to interact with them at all. And the vow can be made such so it is agreeable to your abilities without overwhelming you."

"Alright. Let's hear about archangels."

Archangels! There are several to pick from.

Henry thinks that Scott's innate spell pretty much makes redundant the archangel that provides healing in exchange of pacifism (Lydia is too likely to need to hurt someone). There is Henry's own hallowed vow is obviously useful and Lydia can have more than one vow at same time. There is a survivalist-focused archangel that could improve her sense of direction in relation to her banshee sense, but that depends how much time she wants to invest on learning wild survivalist skills in a town with a werewolf population.

Then Henry snaps his fingers in realization and starts paging through his book until he stops at a page with what looks like an four-winged angel playing a weird cello... except that a second glance reveals that "the cello" is part of his body. This isn't the weirdest archangel in the book. By far.

"Okay, this one was more focused on music an art, but it can also improve hearing, specially the ability to distinguish different sounds. Pretty sure you could use it, at cost of needing to spending some time appreciating music or ideally practice with an instrument as a result it would improve your banshee hearing."

"I should pick up an instrument anyway. Colleges love that sort of thing."

"Really? Is that a cultural thing? Also, are you going to want the telekinesis vow? I was under the impression that you are not as likely as Stiles to suddenly research how people did pottery a thousand years ago in another continent."

"That sounds about right, yes. I did learn archaic Latin, but dead languages are a lot more practical than ancient pottery trivia."

"No, they're not. They're both pointless wastes of time and it's sad that you spend so much time on them instead of solving equations or whatever math people do. You could have your Nobel prize already."

"Fields medal."

What a weirdly cute interaction. "Well, different people have different priorities. More importantly, having compulsive interests on random trivia are not waste of time when you can get tangible magical results. Anyway, Lydia, do you want to make those vows?"

If she says yes, Henry will guide her through the process much in the same way he did for Stiles and by the end of it Lydia will feel the seeds of magic taking place.

She says yes!

The seeds of magic take root.