Flatten chicken to 1/4-in. thickness. In a large resealable plastic bag, combine 1/2 cup lemon juice, 1/4 cup oil, 2 teaspoons salt and 2 teaspoons pepper; add chicken. Seal bag and turn to coat. Refrigerate for 1 hour.
For pesto, place the basil, Parmesan cheese and garlic in a small food processor; cover and pulse until chopped. Add the pine nuts and remaining lemon juice, salt and pepper; cover and process until blended. While processing, gradually add remaining oil in a steady stream. Set aside.
Drain and discard marinade. Grill chicken, covered, over medium heat for 4-6 minutes on each side or until meat is no longer pink. Grill buns, covered, for 2-3 minutes or until golden brown.
Spread 1 tablespoon mayonnaise over cut side of bun bottoms. Layer with chicken, provolone cheese and roasted red peppers. Spread pesto over cut side of bun tops; place over sandwiches.