Chanukah is a unique Yom Tov . On most Yamim Tovim, we don't work. Chanukah is a Yom Tov when we work. And as we've discussed, the time to light the menorah is relatively early. in most locations. So, somebody's working and he can't get out of work, and he has family at home. What should he do, in terms of lighting the menorah, because he's going to have to light the menorah later than the designated time.
So the proper thing to do is as follows. If you have children or other family members who are at home and are lighting their own menorahs, they should light them at their home at the proper time for lighting the menorah. Your not being home should not prevent them from lighting the menorah at the right time.
On the other hand, you should wait till you get home. Not rely on other people lighting the menorah on your behalf. Because it opens up all sorts of difficult questions regarding the bracha, regarding shelichus . Can you appoint someone to light the menorah on your behalf? Can you not? And therefore the best thing to do is just light the menorah when you come home.
And this is particularly true for another important concept. We know when we speak about lighting the menorah, when we speak about Chanukah, a very important element to the Yom tov is Pirsumei Nisa , publicizing the great miracle that Hashem did on our behalf. The poskim discuss that originally the way Pirsumei Nisa was fulfilled was by people in the street outside seeing your menorah.
But today the focus is really more towards your family and yourself. And therefore as long as you and family members are home and see the menorah lit, even though you lit it later than the proper time, you have fulfilled the mitzvah.
For more Chanukah learning:
What can a Menorah be made from?
Am I required to have a seudah on Chanukah?
Candle Lighting When You're a Chanukah Guest