That's what I thought. But they lose their growth after one battle, I'm looking for a more permanent level up. I have been using essences in the meantime.
Last time I played, the Lime Slime couldn't gain levels.
Explaining is hard but the main thing is that the Slime can only grow by consuming potions. Even after a fight, the Slime will retain some points in the stats affected by the potions. Moreover, it stacks so you can feed it a lot of potions before jumping into a fight.