Place each chicken breast half on a sheet of waxed paper; flatten to 1/4-inch thickness, using a meat mallet or rolling pin.
Lightly brown chicken in 1 tablespoon butter and oil in a large skillet over low heat. Remove chicken to a warmed serving platter, reserving pan drippings in skillet. Add lemon juice, salt, and pepper to skillet. Cook over medium heat, stirring constantly, until thickened and bubbly. Stir in 1 tablespoon melted butter. Spoon sauce over chicken.