In a medium saucepan, melt the butter over medium heat. Add the flour to make a roux and cook, stirring, about 1 minute. The roux should have a wet sand consistency. Add the chicken broth and lemon juice. Bring to a boil, then reduce to a simmer and whisk constantly until thickened, about 5 minutes. Set aside.
Season both sides of the chicken cutlets with salt and pepper. Lay a slice of prosciutto on each piece of chicken, spread with some ricotta and top with some spinach. Roll up each cutlet and secure with a toothpick.
In a large skillet, heat the olive oil over medium heat. Sear the chicken, 1 to 2 minutes per side. Add the chicken broth mixture to the skillet and bring the liquid to a boil. Reduce the heat to low, cover, and simmer until the chicken is cooked through, about 10 minutes. Transfer the chicken to a serving platter, remove the toothpicks and spoon over the pan sauce.