Ah, thankyou for the clarification.
The lime slime does not gain levels but instead will consume potions stored in its inventory, it will use these during battles before attacking. Any potions it drinks will apply permanently, unless your party is defeated.
You can buy it from an NPC for 500 gold in the Tavern in town. They are in the back by a fireplace. The Tavern is next to the potion shop.
