This enemy is one of the easiest awakened enemies if not supported by other units. Almost any decent ranged attacker will be able to strike it from a distance. Using just macho cat and wall cat plus dragon cat with any other support cats is practically a guaranteed win.
Strategy 1 (only for 'no frills evolution Hard'):
Macho cat, Wall cat, Samba cat (optional) Dragon cat, Salon cat (optional), bahamut cat (optional, but bring him if you have him as he will speed up the battle a lot) all other cats are up to you, but don't count too much on them if they are close ranged and low health, as Lollycat (enemy) has an area attack and decent range.
At the start of the battle, build up dragons and slowly work up lots of macho and wall cats. When the lollycat comes out of the base, just keep spamming macho and wall, keeping it distracted. Any other cats you bring will kill the peons, allowing your dragons to focus on the lollycat. Lollycat does not have that high health, so you should be able to kill it in under 8 minutes. Unless you want to try the harder stage, bring a treasure radar, and congratulations! You have a new true form!