Cerberus is a family pet of sorts, for it’s seen in chat messages that Lucifer often takes him for a walk and cares for him, like a regular dog. However, Cerberus is implied to be very huge, for Leviathan commented that he felt hot air coming above him when the story first introduces him.
MC, Mammon, Leviathan, and Beelzebub headed for Lucifer's room to take a picture of Lucifer's sleeping face in order for Asmodeus to enter a pact with MC. Upon entering the room, they encounter Cerberus and found the way they came in locked, and escaped through another door which teleported them to the castle's underground labyrinth. It was revealed that Lucifer placed a curse on his door that would transport anyone who didn't knock into Cerberus's domain.
When MC, Mammon, Leviathan, Satan, and Lucifer enter the game Dogi✩Maji✩Memorium, Cerberus served as the final boss but didn’t recognize Lucifer as his master. When he tried to attack Satan, Lucifer’s wrath comes forth and is able to dominate him.
Since the incident with the grimoire, Lucifer has Cerberus patrol the Mausoleum, a fact the brothers and MC did not know when they tried to retrieve the grimoire in order to lure Lucifer out of being under house arrest (Lesson 14).