Season the chicken cutlets with salt and pepper, then coat them in flour. Coat a sauté pan with nonstick spray, add the oil, and heat over medium-high.
Sauté the chicken cutlets 2 to 3 minutes on one side. Flip the chicken over and sauté the other side, covered for 1 to 2 minutes, until cooked through. Transfer the chicken to a warmed platter and cover with foil; pour off the fat from the pan.
Add the wine to the hot pan and then and add the minced garlic. Cook until the garlic is slightly brown and the liquid is almost evaporated, about 2 minutes.
Add the chicken broth, lemon juice, and capers. Return the chicken to the pan and cook on each side for 1 minute. Transfer the chicken to serving plates.
Finish the sauce with butter and lemons. Once the butter melts, spoon the sauce over the chicken. Garnish with chopped fresh parsley and serve immediately.
Notes
*My market sells chicken cutlets already sliced thinly (if you're not into cutting and pounding them yourself, you might look for those). If you have to buy thicker cutlets, cut them in half horizontally and pound them out to an even thickness.
*I don't like to skimp on the oil on this one- you can certainly use less, but I think the chicken turns out to have a nicer crust and a better flavor when sautéed in a good amount of oil. You can always rid the pan of excess oil after sautéing- before you deglaze and make the sauce.