1. In a large skillet, cook the bacon over moderate heat until crisp, about 5 minutes. Drain, then coarsely chop the bacon. In a food processor, puree the bacon, basil and garlic to a paste. With the machine on, add the olive oil in a thin stream. Transfer the stuffing to a bowl. Stir in the lemon juice and season with salt.
2. Make a 1-inch horizontal incision in each piece of chicken to form a pocket. Spoon 1 tablespoon of the basil stuffing into each pocket and press gently to close. Season the chicken breasts on both sides with salt and pepper.
3. Put the flour, eggs and bread crumbs in separate shallow bowls. Lightly flour the chicken breasts, shaking off any excess, then dip them in the eggs and coat with the bread crumbs.
4. In a large skillet, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Add half of the chicken and cook over moderately high heat until browned and just cooked through, about 3 minutes per side; lower the heat if the chicken browns too quickly. Repeat with the remaining butter, oil and chicken. Thickly slice the chicken and serve.