Hmmm. It seems to be that the boss fight in the public version is waaay much harder that the Patreon version was. Reading your comments I have a doubt: why aren't you using Qum? Her buff to both ATK and MAG should help you a lot.... Although, Carina's Mass Heal it's useful, three is no practical gain of buffing your defense.
I must be missing something...
I think I read that Sierra boosted the difficulty of the fight after feedback from Patrons. Qum would probably be a better choice than Carina thanks to that buff. I suspect people have been avoiding the succubi vs. HL because she seems like the sort of person who would be strong against succubi. I got tired of dying, so I was just using what others said had worked. In a replay, I'd probably recommend a Qum/Varia/Aka party versus HL. You'd also want to buttplug Qum to insure she starts with full lust, so you can use that first turn to use Arousing Aura.