Santa Lily or Eli chan

I literally have the exact same question pretty much, as I also have an Eli Lancer NP3, and with her improved Sadistic Charisma and augmented NP, I feel like she actually does stand up just fine to Jailter.

I'll wait for someone to answer since I also had this inquiry, but I do think you brought up one of the defining differences yourself, which is that Bathory is going to give better offensive support to the party, while Lily may edge her on raw damage because of Ephemeral Dream being such a strong buster buff. I think both lancers have a support niche, but Liz's is for offense and Santa Lily's is a little more geared towards healing between her healing skill and her NP.

If I had to guess, I feel like Lily is still gonna edge it on NP damage, since Liz's charisma double buffs other females, but not herself. So I think Ephemeral Dream's 55% buff at max wins for sure (especially for you since it's NP5 vs NP2 with the same multiplier, with my Liz at NP3 I think it's even closer). I do think Liz edges her overall though because of a better offensive support skillset and her guts. In fact, I think they'd go very well together, since Liz can double buff Jailter and they can clear archer waves in conjunction when required.

For Eli, you aren't going to get 500% dmg @ NP2 right now. You have to wait until the interlude at 2020.

Elizabeth Bathory's defense debuff can also be resisted.
Eli's skills are also harder to level than Santa Lily, Eli requires Forbidden Pages which you should be saving for better caster servants.

Overall I think Santa Lily will be better for farming and nuking enemies now, and you can always wait until 2020 for Eli's NP interlude.

Acutally, i prefer Liz as female servants’ offensive support. I never expect her NP will do a great damage even though i have her np5.
Jalter santer do slighly better job on aoe farming, also she has np charge skill (but dont really need upgraded).