Mix together flour, lemon pepper and salt in a shallow bowl or plate. Dredge chicken breasts in flour mixture, shaking off excess.
Heat oil in a large skillet over medium-high heat. When it begins to shimmer, add the chicken breast in a single layer, without crowding the pan (may need to brown in 2 batches) and cook 2-4 minutes per side until golden brown and there is no longer any pink. Remove the chicken to a plate and loosely tent with foil to keep warm.
Add chicken broth, lemon juice, and sugar and bring to a boil, stirring to scrape up all the brown bits on the bottom of the skillet. Bring to a boil then add cornstarch/water mixture and continue to boil until thick, about 1 minute. Remove from heat and add butter and stir to melt. Return chicken to pan. Garnish with chopped parsley and lemon slices and serve.
