Coming to English via the French word meaning the same, this word is thought to derive ultimately from the Latin word lamella, a "thin plate," referring to the long, flat shape of the omlette, and to represent a gradual corruption of allumelle first to allumelette, then to alomelette (Le cuisiner francois of 1651 has aumelette). The modern term "omelette" appears for the first time in Cuisine bourgeoise of 1784.
Fascinating isn't it ?