Season chicken on both sides with salt and pepper. Pour the flour into a shallow bowl and dredge the chicken in the flour on both sides.
Heat the olive oil in a large skillet set over medium. Add the chicken and cook for about 5 minutes per side, until golden and cooked through. Remove to a plate and tent with foil to keep warm.
In the same pan, melt 1 tablespoon butter and add shallot. Sauté for 2 minutes, then add lemon juice and chicken broth. Scrape the bottom of the pan to release any stuck bits, and bring sauce to a simmer.
Once sauce is slightly reduced, remove from heat and whisk in butter and salt and pepper to taste. Add lemon slices and return chicken to the pan, spooning sauce over the top.
Serve chicken with more sauce over the top, lemon slices, and chopped parsley.