|The Aruch Hashulhan (halachic work by Rabbi Yehiel MichelEpstein,1829-1908, OC 670:8) discusses the case of someone who did not light one night of Chanukah. He rules that he has lost the misva for that day. There is no significance to lighting the next day, because the obligation is only at night. Even if he would artificially create a darkened room, there is no misva.|
However, he can and should continue to light on subsequent nights with a beracha. Even if he missed all seven nights, on the last night he would light eight candles with a beracha. This ruling is a rejection of the opinion brought in the Beit Yosef that compares the halacha of Chanukah with Sefirat HaOmer. If one forgot to count a day of the Omer, he does not continue to count with a beracha.
The Aruch Hashulhan explains that the nature of the obligation of lighting on Chanukah is fundamentally different from the obligation of counting the Omer. The emphasis of the Omer is on counting consecutive days. Therefore, if one forgot a day, the entire series is lost. Whereas, on Chanukah, each night stands by itself. In fact, the primary obligation is only to light one candle for each night.
SUMMARY: If a person missed a night of lighting on Chanukah, he does not light the next day, but he does continue to light on subsequent nights with a beracha.