Whisk together 1 cup of the flour with the paprika and some salt and pepper in a large bowl. Dredge the chicken lightly in the flour mixture, shaking off any excess.
Heat a medium skillet over medium-high heat. Add 1/4 cup olive oil and heat until it starts to shimmer. Sear the cutlets on both sides until browned, 1 1/2 to 2 minutes per side. Remove the chicken to a plate and set aside.
Place the skillet back over medium heat and stir in the remaining 1 tablespoon flour. Add the wine and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Bring to a simmer and cook until slightly reduced, 1 to 2 minutes. Stir in the capers and bouillon cube, then add in the seared chicken and any juices and 1/4 cup water. Simmer, flipping the chicken halfway through, until the sauce is reduced slightly and the chicken is cooked through, about 3 to 4 minutes
Heat a grill pan over medium-high heat. Drizzle the pan with olive oi and grill the lemons until caramelized, about 2 minutes per side. Serve the piccata sauce over the chicken and garnish with the grilled lemons and thyme sprigs.