I couldn't kill Lilly with any of the rabbits I have so used a Pygmy Cow. Stampede and Udder Destruction works every time. However the snails still proved troublesome as well but after a few tries with bad RNG I finally got it along with my Family Battler achieve!
Use S/S rabbit, and use nether roach 1,x,x as third pet, nether roach spam nether blast, it is still a bit of RNG depends if ticker is faster than rapana whelk, as ticker without flying speed buff is same speed as rapana
Worked with a fast rabbit, I used Spring Rabbit as didn't have a levelled Noblegarden Rabbit. With a slower rabbit Lilly killed my first two pets and I surrendered, you need a rabbit faster than Lilly.
S/S Noblegarden Bunny killed Lilly nicely, but Ticker killed S/S Rapana Whelk before Acidic Goo was applied and then proceeded to kill H/H Scooter the Snail with Bloodfang and killed Noblegarden Bunny with Claw as soon at it entered the fight as Ticker was still faster :( Second try went better, as Ticker was at 441 health when Noblegarden Bunny came back, making it faster thus allowing Dodge to be applied and Ticker died after two rounds of Flurry
Used Bush Chicken with 1, 2, 1 and started with cyclone so that there was some damage to Ticker before the snails were in. Flock mostly took out Lily and then finished with ooze touch then went as above with acidic goo, ooze touch and dive when can