We lost someone whom we loved dearly and we are also honoring the family's way of grieving. However, we'd like to light the Menorah we recently purchased in his memory this Dec 2nd. With much respect and reverence, I would simply like a yes or a no if doing so is dishonorable to your faith.
Thanks for your consideration in asking this ahead of time. It seems to me that, not only would it not be disrespectful to light a Chanukah menorah in memory of your friend, it would be fairly traditional. Although the idea behind a menorah is to remind people of, or advertise, the miracles that Chanukah celebrates, it is, after all, a burning lamp, which is used traditionally to memorialize the dead. Just make sure you light it in a safe place and manner.
Assuming you aren't Jewish, there would be no mitzvah (commandment) for you to light the menorah, but I don't see anything wrong with it. I will add that perhaps the best way to honor your deceased friend is doing good deeds in his name, like tzedakah (charity).
Take a look at this webpage to learn how to light the menorah. Just one catch, though - since you aren't Jewish make to sure to not recite the blessings.
The Short version:
Lighting a 7-hand Menorah on Chanukkah at home IS dishonorable in the Jewish Faith and it contradicts the Jewish Law.
THe Long version:
We hold that the biggest remembrance and practical benefit for the soul of the diseased is TORAH and Mitzvot and good deeds.
The best way to remember a person is by organizing TORAH learning in public in his/her name, do Mitzvot yourself or pay others to do Mitzvot, especially pay to learn Torah and say Kaddishim, promote positive activities like volunteering or helping the needy or Tzedaka etc.
Lighting a 7-hand Menorah at home has no meaning and no tradition in Judaism since the destruction of the Temple and it is explicitly forbidden to light at home as it is תבנית כלי קודש. See Rambam הלכות בית הבחירה ז, י and Shu"A יו"ד קמ"א.
Lighting a 8-hand menorah is dedicated to Chanukkah as a distinctive Jewish festival and can not be used for mourning. It is clearly forbidden for Jews to light a 7-hand Menorah for Chanukkah candles!
If you don't care what Judaism says and want to do what you want, you're free to do it your way, but remember it would be a much more useful remembrance if you spend the money on Tzedakkah instead of the oil or candles.