To the purist, a lager should be brewed with a S. Pastorianus strain of yeast and an ale with S. Cerevisiae strain of yeast. The former ("lager yeast") works at far lower temperatures than the latter "ale yeast") does.
That said, the first lagers (in Bohemia in the 1500's or so) were brewed with whatever yeast happened to end up in the beer. Nobody knew what yeast was in those days, or even that it existed. The term "lager" (as has already been mentioned in responses above) refers to the German word for "storage" (Lagerung) and stems from the fact that this beer style was brewed seasonally, then packaged in sturdy wooden barrels that were stored deep in the cool caves occurring in the region for months on end. During this lengthy maturation the beer fermented out further, cleared, and became somewhat carbonated, which eventually led to beer (esp. later) as we know it today. Until then, beers were brown, murky, flat concoctions served at room temperature.
While using an ale yeast for a later is a vile abomination to the purist, the truth is that quite a significant portion of the micro-brewed beers in the world sold as lagers are in fact fermented with S. Cerevisiae, but using a variety suitable for lower temperatures, in order to obtain a more neutral and "cleaner" flavor profile. Lallemand's Nottingham Ale Yeast (no rebranded to High Performance Ale Yeast) is a good example: at room temperature it's a typical ale yeast giving you a measure of fruity flavors that work well in ales, but at the lowest end it of its wide temperature range (about 10C / 50F or even little lower) and a proper diacetyl rest, it will produce a beer with a flavor profile generally indistinguishable from lagers fermented with a "real" lager yeast.
So the only real question, as I see it, is whether you want a beer that tastes, smells, looks and drinks like a lager and has all the vital characteristics or a lager, or instead you want to make a big think about the pedigree of the yeast you used to brew it. Your choice. :-)