Luc's Parents are the unseen, unnamed mother and father of Luc Maxwell. They have gone on a three day vacation, leaving Claire in charge of their son. The series and loop takes place on the second day.
In "Port Fear", Luc left an exploding cake in the fridge, which went off on Claire and the entire kitchen. Claire demanded that he gets the kitchen cleaned before his parents returned tomorrow, and Luc laughed, promising he would, knowing tomorrow would never come. Claire then received a phone call, from Mr. Maxwell. His voice was simply sped up phone gibberish, but Claire made it obvious that he said that he and Mrs. Maxwell would be extending their vacation to an entire year, forcing Claire to babysit Luc for all that time, making her worst fear become a reality.
In "Zap's Day Off", Claire rambled about how she needed to get the car fixed before Luc's parents came back tomorrow.
In "Rocket to Tomorrow", Claire mentioned Luc's parents again.
In "A Glitch in Time", Luc and Theo touched upon the fact that Luc hasn't seen his own parents in an unnaturally excessive amount of days, which made him grow very attached to Leo in the way a child would to a parent.