Season chicken cutlets really well with salt and pepper, then dredge both sides in flour, shake off excess and add to a clean plate on the side.
Heat 2 T butter and 2 T oil in a large heavy bottomed skillet over medium high heat, until sizzling. Working in batches, add 3 chicken cutlets and cook for 2-3 minutes a side, until golden. Transfer to a plate on the side and cook remaining 3 cutlets. *You may need to add another T of butter and olive oil at this time. Transfer to the same plate on the side.
Now, add lemon juice and white wine to your skillet, and using your spoon, scrape the brown bits off the bottom. Bring to a boil, then reduce heat and simmer for 2-3 minutes.
Add in remaining 2 T butter and capers and stir until butter is melted.
Add chicken cutlets back to the skillet along with a few lemon slices, and spoon the sauce all over the tops. Reduce heat to low, cover and simmer for 10 minutes.
Adjust salt and pepper if needed, and option to garnish with fresh parsley.
Serve with roasted vegetables, side salad, pasta, etc.!