Flatten each piece of chicken between two pieces of waxed paper with a meat mallet, or even easier, have your chicken guy at the market flatten them.
In a medium bowl, beat together eggs and the juice from 1 1/2 of the lemons (reserve remaining lemon for later). Slowly beat in enough flour to make a smooth batter about the consistency of pancake batter. Season with salt and cayenne pepper.
Heat about a 1/8" thick layer of olive oil in a large skillet. Dip chicken pieces in batter and fry in oil, turning only once as sides become deep golden brown. (You'll only be able to do two at a time, so keep cooked pieces in a warm oven). Just before serving, sprinkle with the remaining fresh lemon juice. Serves 4.
Serve with a big pile of steamed green beans sprinkled with toasted almond slivers.