Combine the panko, almond flour, lemon zest and 1/2 teaspoon each salt and pepper in a shallow dish, using your fingers to evenly blend the zest into the crumbs. Lightly beat the eggs in a separate shallow dish and season with salt and pepper. Season the chicken with salt and pepper.
Heat about 1/3 cup olive oil in a large nonstick skillet over medium-high heat (it?s hot enough when a pinch of panko sizzles when it hits the oil). Working with 2 or 3 chicken breasts at a time, dip each piece in the beaten egg, letting the excess drip off, then press the chicken into the crumb mixture to coat. Add to the hot oil and cook until browned and cooked through, 1 1/2 to 2 minutes per side. Transfer to paper towels to drain. Reduce the heat if the chicken is browning too quickly and add more olive oil as needed between batches.
Toss the greens, fennel, apple, basil and red onion with the lemon juice and the remaining 1 tablespoon olive oil in a bowl; season with salt and pepper. Divide the chicken among plates and serve with the salad and lemon wedges.