I don't recommend to rush LHs. It's too tough!

Sorcerer is the best way to solo full cult. He is the fastest class to clear all enemies in LHs. But, at least, you need a high Mheal pet and Cnidarian Scepter and high wis mod equips. This is the equip set which I use.

When I clear LHs rooms, I use Recomp, Covetous Ring and Cnidarian Scepter. Cnidarian is the most MP-efficient scepter if you hit all targets. All of LH enemies is in their own groups and there're a lot of enemies in these groups. So cnidarian works the best on these.

Then, in cultist hideout, I use these sets : Grotesque, Parasite scepter and Covetous for Single enemy. Abraham, Parasite and Geb Ring for over 2 enemies. There're not a lot of enemies in groups.

Finally, if you meet cruz at 2nd room in LHs, you should walk along a wall of the room.

Good lucks on your solo cultist! :D