Yes, but what kind? Bear fat? Hog fat? Which is best? Maybe they didn't know as much as we know, but they knew stuff we never even thought of, and knew it when it counts. It would be total tragedy for the chariot wheels to seize up in the midst of battle because you used sheep fat instead of camel hide soaked in hot bear grease.
In the biblical account of the Egyptians following the Hebrews into the parted Red Sea before becoming fish food, some versions read that God made the chariot wheels jam. The mad Pharoah had probably ordered the Egyptian army to drive the chariots well beyond their regreasing limits and the slogging in the wet sand couldn't have helped.