Now that there is no more bonk bat how do you win fights in Lillith difficulty ?
The bonk bat is in the game, you probably just have Silly Mode off.
Lilith is a meme difficulty since the game is presently stupidly unbalanced even on normal difficulties, so personally I wouldn't really fret trying to make it work. Overall, the best way to win fights in general is to do Melee Weapon Soldier to oneshot just about every fight, and then getting enough shielding to not fall over instantly. Transforming into more powerful races, such as horses, alicorns, gryphons, and especially later on dragons, will also greatly improve overall combat ability (EDIT: or become a slime, and transform to whatever you want whenever you want. That's probably a better idea.).
An important thing with Lilith is cheesing the fact that if you draw (both sides all get knocked out), you win. For an example, police fights are occasionally straight-up unbeatable, as the cops' Seven Rounds Rapid attack can roll some absolutely preposterous numbers that you cannot survive without cheating in extra HP shield or something.
Honestly, I don't know how far you can actually progress without turning off enchant capacity and buffing yourself to the gills. Methinks you'll hit a wall around trying to do the Meraxis quest: those imp fights can be scary, and I don't think you can cleave well enough before you're bursted down.