i lost the first time as RDM/BLM at 20%, i took too much hate and took a lv holy in the face.
2nd time i went with meds, and it worked, just take alot of +MP and -enmity so lilisette can keep hate.
If you stay far enough you wont get hit by Lv holy.
The only problem is that Lilisette is weak as hell after atomos for like 45sec, so she drop from 100% to 70% fast so need to spam more cure.
Also RDM/SCH works well for MP save with Light arts and Penury
A taru RDM/SCH in my ls solo'd it. It helps to keep her at high HP and then when the thing comes out it won't suck you off if you don't cast on either of them. I also noticed that what it actually appears to do is drain all of your stats so they are at 1, then it gives them to the main enemy before despawning. That's why it's attacks seem to increase.
Spoiler: show
Duo'd this as blu/whm and brd/whm with a bunch of meds, I'd imagine that a rdm with some meds and at least one source of auto-refresh should be able to solo this. If you dont get your stats taken by atomos its easy, if you do cait will deal a lot of extra damage to lisette and drain your mp.