Lili's attack power scales with INT and equipping a shoe weapon will add that damage together

Shoe weapon seems not work but INT does work though.

Here's a fun fact: Around the late game (I suspect it to be after either learning Invert or Dimension Shift) you can perform an upwards leap like in Symphony of the Night. If you go to Libre Ex Machina and enter the room right underneath O.D.'s, you can perform this high-jump to toss him off his chair from below.
Which is a reference to Symphony of the Night, where you could do the same thing to the Librarian.

Another fun fact: All cutscenes in Bloodstained use the in-game model, and triggering a cutscene does not break the Bunnymorphosis, so you can watch all those serious moments in the game take place with Miriam turned into a demonic Bunny one costume-slip away from a Playboy-Cover.

I'm pretty sure reaching rank 9 improved the lighting kick move, being way faster.

Trivia: in Castlevania SotN Axe Lord Armor shares the similarity with Bunnymorphosis where alucard transform into Axe Knight

Another bonus: the Rul'sha demoness enemy's with bless you with a strength boost if you are a lili.