This site provides the following etymology:
In any event, the Yiddish לאטקע (latke) came from the Ukrainian оладка (oldka), which several online dictionaries faithfully translate as pancake, fritter, flapjack, and the like (muffin seems to be in there too for some reason). This is a diminutive of the Old Russian оладья (olad'ya).
Now it gets interesting: this comes from the Greek ελαδια (eladia), plural of ελαδιον (eladion), meaning "a little oily thing", "a little oil", or "a young olive tree". Which proudly paves the way to eladion being a diminutive of elaion, "olive oil", which in turn comes from elaia, the (Ancient) Greek for "olive".
So, centuries later, five languages away, and twice miniaturised, we get our "little tiny things made of (olive) oil" - latkes.
This article in The Forward gives a little more background on the latke:
The distance from the Yiddish latke to the Greek elaion is about as vast as Diaspora itself, but the relationship is interesting because the first latkes were little cakes made from curd cheese and fried in butter or olive oil. (Eating cheese on Chanukah is said to refer to the Apocryphal story of Judith, who fed salty cheesecakes to the Syrian general Holofornes to make him thirsty, and then plied him with wine until he was so inebriated she could chop off his head with a sword; this symbolic connection, though, was not made until many centuries after the first cheese latkes.) As Jews began to migrate eastward into Eastern Europe, butter and oil grew increasingly precious and expensive, and poultry fat became the chief frying agent; this made the use of cheese off-limits, and so by the Middle Ages latkes were most often made not from dairy ingredients but rather with a simple batter made from buckwheat flour (recall the original Russian meaning of "a flat cake made from unleavened wheat flour").
One thing that neither of these articles mentions is that the English words "olive" and "oil" both derive from elaion (as do parts of the words petroleum and Vaseline). So while the custom of eating latkes might not go back to olive oil, certainly the name of the word does...