I'm assuming Vlad much like Martha isn't happy with being with such an anti Christian god group so was holding back as much as he could
Ehh sort of. Jeanne Alter is a really shitty Master so her "Servants" chafe at following her orders, and despite his legend Vlad is a firm believer in Noblesse Oblige. He also has immense respect for Christian Saints, like Jeanne or Martha. Think of Jeanne Alter's minions being forced to obey her like Artoria was forced to obey Kiritsugu or Cu obeying Kirei. They have no desire to follow her orders they are still
Heroic Spirits after all, but the Madness Enhancement and command seals force their obedience. So letting the team get away when he can without getting under too much suspicion is pretty much all Vlad could do.
Incidentally this is probably the last time Taylor and the Team will get
this lucky, at least without some serious sacrifices occurring. Everyone else from here on will be firm believers in trying to fuck over everyone else. Not sure if there's something similar that happens in Canon Septem, and even my fantastic savant memory isn't that good. Altera doesn't go all out, but I think it was because she didn't particularly want to attempt to win. Could be wrong on this last part, but a no holds barred Altera is easily up there in terms of destructive capabilities as Gilgamesh.
That spinning death beam Noble Phantasm attack you see in the game of Grand Order? That's not a
real Noble Phantasm. No that's Altera purposely holding back and using a fraction of her Noble Phantasm sword's power.
Even Teardrop Photon Ray, the attack we see Altera use in the Final Singularity and in the Extella games, isn't a true Noble Phantasm. Nope instead that's just Altera
purposely attracting the attention of the dead god Mars and using her own Prana to brute force her way into spoofing her location to above her chosen target and letting the leftover programming from the dead Mars unleash a devastating attack in an attempt to kill Altera, his hated enemy. She just misdirects it so it hits her enemies instead of her. It's a final "fuck you" from him to her ala a Dresden style Death Curse, albeit a perpetual one.
Ah... Carmilla...
Well, hopefully we'll see Liz in the future.
Liz is in Orleans, along with Kiyohime. They're just over in Charite I think.