Combine the lentils, eggs, and salt in a food processor. Puree until the mixture is the consistency of a runny yet textured hummus. Pour into a mixing bowl and stir in the onion. Add the breadcrumbs, stir, and let sit for a couple of minutes so the crumbs can absorb some of the moisture.
At this point, you should have a very moist mixture that you can easily form into twelve 1 1/2-inch-thick patties. You can always add more bread crumbs a bit at a time to firm up the dough if need be. Conversely, a bit of water or more egg can be used to moisten the batter.
Heat the oil in a heavy skillet over medium low, add 4 patties, cover, and cook for 7 to 10 minutes, until the bottoms begin to brown. Turn up the heat if there is no browning after 10 minutes. Flip the patties and cook the second side for 7 minutes, or until golden. Remove from the skillet and cool on a wire rack while you cook the remaining patties. Carefully cut each patty in half, insert your favorite fillings, and enjoy immediately.