I found a friendly slime once but then i lost to the lich and haven't come across it since, is there some requirement or is there just a small chance? (By losing to the lich I was booted to the main menu and hadn't saved yet)
Have you gave the slime a potion when talked to? If so, you gotta leave the lich cave and the slime will be at the entrance. Keep giving potions until you have the option to add them as an ally.