Why is Liandry's getting changed? (an issue with max % hp burn)
Liandry's Torment was a great pick. Some people would buy it for the +15 magic pen, sure, but the real appeal of buying it was for its current health burn. This made it exceptionally well suited for countering enemy champions that built a lot of hp. It was a counter item. Fun and balanced because you wouldn't get the most out of the item if you built it against low hp champions, (unless you ran to late game).
I'm not going to tackle the 'Essence Drain' passive, because that's a can of worms on its own. All I will say is that it adds way too much value to the item.
Now moving onto the issue of changing this passive from 'current health' to 'max health' burn. The reason max health items don't work on ap champions, is that DOT abilities make it BROKEN (apparently you've said you want to make DOT like that though, so why?). Max health items like bloodrazer and to some extent BoTRK work well on AD champs is because they have to consistently attack the enemy to get the most out of it, they're not an ap champ with a single button press and 70% of their hp will go because they built the new liandry's.
Riot what you've done is taken something that used to be a good counter item and turned it into an item that will be good to buy 100% of the time.
Change it back to current health. You will have a better chance at balancing this item.