If a son lives with an elderly mother, can the son light one menorah and also thereby be yozei the mother for hanukah lights. Is there a problem with this?or should each one light separately?If the son comes home late, can his mother light for him when she lights earlier and he not light at all?
He can certainly light on behalf of his mother.
The general custom is that only the men of the household light the Chanukah menorah, and if the son is the only man in the household his lighting has the same halachic status as a father’s.
If the son is coming home late, it is fine and correct for the mother to light at the right time, and the lighting is effective for him to fulfill the mitzvah.