The answers to this question explain that if one is not eating at home during Chanukah, he nevertheless needs to light at his house, where he will be sleeping that night.
What happen if someone switches his 'home' during one of the nights of Chanukah?
As a concrete example, consider someone who owns two houses in two cities. He has been living in his house in City A for the past two months, and at sunset/nightfall is planning to leave his house later that night to move to his other house in City B for the next two months.
Does he light at sunset/nightfall in his first residence (where he has been sleeping on the previous nights)? Or in his new residence where he will only arrive later that night and where he will be sleeping from now on? (Or maybe he doesn't have an obligation to light at all?)
Does it make a difference how late at night he plans to move? Does it make a difference where he will be eating that night?
(Assume that this person forms his own household (or is traveling with his entire household) such that relying on others to light on his behalf in either location is not an option.)