(Building on my comment, at Isaac's suggestion:)
The Or Zarua isn't saying that the oil with which the miracle occurred wasn't used for lighting the menorah. Indeed, he quotes the narrative in Menachos about how the Chashmonaim created a temporary menorah out of iron spits and used it for the lighting. (Bear in mind that iron is not to be allowed to touch the Altar - Ex. 20:21 and Deut. 27:5; Rambam, Hil. Beis Habechirah 1:15-16.)
He simply says that the miracle had to last for eight days, because for seven of those days they were busy rebuilding and rededicating the altar, and therefore had no time to prepare new other oil; and he goes on to say that the holiday is called "Chanukah" in honor of this rededication.
This use of oil for lighting was, of course, the continuation of the mitzvah recorded in the Torah (Ex. 27:20-21, Lev. 24:1-4) to light the menorah daily in the Mishkan, and later in the Beis Hamikdash.