In a large bowl, whisk the lemon juice, rosemary, thyme, garlic, 1 tsp. sea salt, 1/2 tsp. black pepper, and the crushed red pepper. Add the chicken; turn to coat. Cover and chill, turning occasionally, at least 1 hour and up to 2 hours.
Drain the chicken, leaving any marinade that is clinging to it. In a wide shallow bowl, beat the eggs. In another wide shallow bowl, whisk the flour, 1/2 tsp. sea salt, and 1/4 tsp. black pepper. Working with 1 piece at a time, dip the chicken in the eggs, then dredge in the flour mixture to coat. Place on a baking sheet.
Set a wire rack inside another baking sheet. In a large deep skillet with a lid or medium Dutch oven, add enough oil to come about halfway up the sides. Heat the oil over high until a deep-fry thermometer registers 350°. Using tongs, carefully add the 4 breast pieces to the oil. Cover and fry the chicken until golden on the bottom, about 4 minutes. Uncover, turn the chicken, and fry until golden and cooked through, about 3 minutes more. Transfer to the rack. Repeat with the remaining chicken, cooking for 4 minutes covered, turning, then frying uncovered until golden and cooked through, 4 to 6 minutes. Season and let cool for 5 minutes. Serve with lemon wedges.