Season the chicken with salt and pepper. In a shallow bowl, combine the flour, garlic powder and paprika. Roll the butter slices in the flour mixture and set aside.
In another shallow bowl, beat the eggs with the cheese and the juice of 1/2 lemon.
In a large skillet, heat the EVOO, three turns of the pan, over medium to medium-high. Dredge two chicken breasts in the flour, then coat in the egg mixture. Cook until deep goldenbrown and cooked through, 2 to 3 minutes per side. Transfer to a plate. Repeat with the remaining chicken, flour and egg mixture.
Add the lemon slices to the skillet and cook until browned, about 2 minutes per side. Transfer to a plate. Add the garlic to the skillet. Stir 1 minute, then add the wine and cook, scraping up any browned bits, 1 minute. Add the stock, bring to a simmer, then cook 2 minutes. Add the flour-coated butter and swirl in the skillet to melt. Simmer until the sauce thickens slightly, 1 to 2 minutes.
For the salad, in a large bowl, season the shallot with salt and pepper. Let stand until juices form, about 5 minutes. Whisk in the mustard, lemon juice and vinegar. Whisk in the EVOO and season. Add the lettuce and herbs; toss to coat.
Divide the chicken among plates. Pour the sauce over the chicken, then top with the lemon slices, salad and crispy onions.