The Poskim bring down that on Friday of Hanukah, it is preferable to pray Minha Gedolah-early afternoon Minha, before lighting the candles. Different reasons are given for this practice. First, that corresponds to the sequence of service in the Bet HaMikdash-first the Korban Tamid Shel Ben HaArbayim-the afternoon offering was brought, and then the Kohen would light the Menorah. So too, Minha, which corresponds to the afternoon offering, should be prayed before lighting candles, as is the practice the rest of the week.
Moreover, the Peri Megadim (R. Yosef Ben Meir Teomim, 1727-1792, Poland-Germany) says that if one would pray Minha after lighting the Hanukah candles for Friday Night/Shabbat, it would create a "Tarteh D’satreh"-an internal contradiction. How can one light the candles for the next day-Shabbat- and then go ahead and pray the weekday Minha, which is the prayer of the previous day-Friday?
Interestingly, the Mishna Berura, in his Sha’are Sion (679:7), comments that it is only a contradiction if one lights early, at Plag HaMinha, because he is showing that he accepts Plag HaMinha as the start of the next day. However, if he lights ten or fifteen minutes before sunset, that does not indicate that he has already begun the next day. He is only lighting then because he has no choice, as he cannot light candles after Shabbat begins.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) in Parashat Vayeshev says that praying Minha on Friday of Hanukah after lighting Hanukah candles is "Minhag Borim"-the practice of the ignorant. Hacham Bension understands this to refer to a case in which he lit at Plag and then prayed, which is a "Tarteh D’satreh." However, if he would light candles close to sunset, there is no problem praying Minha afterwards. Even so, it is still preferable to pray Minha early because of the first reason.
SUMMARY
It is preferable to pray Minha early on Friday of Hanukah, before lighting candles. If one intends to pray Minha later, he should light Hanukah candles 18 minutes before sunset.
