Brutus is the terrier dog belonging to Eve.
Larry Laffer first met Brutus when the dog peed on his leg, just as was leaving Lefty's in Lost Wages. Although at the time he didn't know the dog belonged to Eve. Brutus was free and wandering about the city.
Some time later, after Laffer met Eve, he decided to follow her back to her home in Los Angeles and move in with her (without her knowledge). She returned home to discover him mowing her lawn. She did not want the stalker moving in so she sicked Brutus on Larry.