By Sefiras HaOmer, there is a dispute whether it’s a single Mitzvah to count fifty days, or whether one fulfills the Mitzvah of counting each day independently (Rosh, Pesachim 10:41, et. al.). As a practical difference, if one forgot to count one night, or if one became a Bar Mitzvah in the middle of counting, can he continue counting - according to the former position, the answer would be no, while according to the latter position, the answer would be yes.
Does this dispute extend to Menorah? Do Rishonim or Geonim address whether it’s one Mitzvah to light Menorah for eight days, so if one missed a day he would be unable to continue lighting, or whether it’s one Mitzvah performed eight times, so if one missed a day he would be able to continue lighting?
Looking specifically for sources which directly state that one can/cannot continue lighting on Chanukah for this specific reason.