TLDR: Crimson Geode 121 Feedbackx2 > Amplify > Stonerush for first pet
Rest of the fight as normal
Yeah this was a tough fight. Didn't have living sand, tried some of the stuff from the comments below but none seemed to work for me.
The winner for me was to swap in for first pet Crimson Geode (P/H) 1.2.1 and in four turns knock out Lilly. Use Feedback until her health is below ~960 (Took x2 for me), then Amplify Magic, then Stonerush. The rest of the fight follows as normal with the strategy turns above.
The biggest challenge on this fight seems to be not letting Lilly get that a heal off at the start or if you do let that happen you need a pretty tank-like pet to withstand the assault.
Thanks Karibean for Electrified Razortooth suggestion. Mine didn't kill Lily, but just went with it until won fight. I have 2 fetid waveling and I should have use both. They are strong for this fight against the last two.
I used Electrified Razortooth (1, 2, 2) as my first pet, and opened with Lightning Shield, Rip, and Blood in the Water. That killed Lilly - her crits worked against her by hitting her with Lightning Shield an extra time. Molaze switched in my Kirin Tor Familiar (2, 2, 1), which I had as my third pet, and I used Arcane Explosion until Molaze switched in my Tiny Snowman (2, 1, 2). Two Magic Hats on Molaze and then two more on Ticker finished the fight.
There might be some RNG at the very beginning, as the ideal situation is Lilly using Toxic Skin on her first turn instead of hitting you before you can get Lightning Shield up, but it might work anyway. But if there's gonna be RNG, I definitely prefer it at the very beginning. Less time wasted before a do-over.