Heat oven to 170 degrees. Line a cookie sheet with foil, and place rack on top. Set aside.
In a shallow plate, mix ½ cup flour, salt and pepper with fork.
Pat sliced chicken pieces dry.
Dredge chicken in flour to lightly cook. Shake off any excess flour.
In a large fry pan or skillet placed on stovetop, heat the vegetable oil over medium-high heat.
Add additional oil if needed, enough to coat bottom of pan.
When oil is hot, gently place floured chicken slices in even layer in pan.
Cook until light golden brown, then turn and cook through until meat is done, approx. 5 minutes.
Remove chicken from pan and place on rack in cookie sheet.
Keep warm in oven.
Meanwhile, wipe excess oil from pan with paper towels.
Melt 3 tablespoons butter in pan over medium heat.
Add garlic. Whisk in 3 tablespoons flour until smooth.
Slowly add the chicken broth, whisking constantly until blended.
Add lemon juice, parsley, additional 1 tablespoon butter, and capers.
Continue to cook until thickened and heated through.
Remove chicken from oven and place pieces over sauce in pan.
Garnish with lemon slices and additional parsley, if desired.
Keep warm in oven until ready to serve.