Place the chicken cutlets between 2 pieces of plastic wrap. Pound to 1/2 inch thickness.
On a plate, mix together the all-purpose flour, lemon pepper, garlic salt and onion powder. Coat the chicken pieces with the seasoned flour.
Heat 1 Tbsp of butter and a couple of drizzles of olive oil in a large skillet. Fry the chicken in batches [ 3 pieces at a time] for 2-3 minutes per side until golden. Remove to a platter. Repeat 1 Tbsp butter and a couple of drizzles of olive oil for the second batch.
Place the lemon slices in the pan and brown on both sides. Remove from the pan.
Add the remaining 2 Tbsp butter, chicken broth, lemon juice and chopped tarragon to the pan to deglaze. Scrap any brown bits off the bottom of the pan. Allow to simmer and reduce slightly. Return the chicken to the pan and spoon the juices on top.
Sprinkle with the remaining chopped tarragon.
Serve immediately over rice pilaf or pasta, if desired.