Combine 1/2 teaspoon oregano and 1/4 teaspoon pepper, adding salt if desired. Sprinkle evenly over top of chicken.
Heat 1 tablespoon oil in a 10-inch skillet over medium-high heat. Add chicken to pan, seasoned-side down. Cover and cook until browned, about 6 minutes. Turn chicken over, and top each breast with 2 lemon slices. Cover and cook 6 minutes or until a thermometer inserted in thickest part of chicken registers 165 degrees F. Place chicken on a plate; cover loosely to keep warm.
Heat remaining 1 tablespoon oil in skillet over medium-high heat. Add sun-dried tomatoes and garlic; cook 1 minute, stirring constantly. Add rice, chicken stock, remaining 1/2 teaspoon oregano, and remaining 1/4 teaspoon pepper to skillet. Gradually add spinach, stirring gently until spinach wilts. Nestle chicken breasts back in skillet. Sprinkle with cheese and pine nuts.