Place the flour in a large ziploc bag, season with salt and pepper. Add chicken, close tightly, and shake to coat.
Heat 1 Tbsp Oil in large skillet until hot. Remove the chicken from the flour using tongs, reserving the remaining for later. Add chicken to the pan and cook, 5 minutes or so to a side, until they are golden brown. Remove to a plate, keeping the frond in the pan.
Add the remaining oil and butter to the skillet, and once the butter is melted, add the onions and thyme. Cook for 2-3 minutes until softened and fragrant.
Add the flour to the onion and cook, 2-3 minutes. Pour in the chicken stock and lemon juice, bringing to a boil while scraping up the good stuff from the bottom of the pan. Reduce to a simmer.
Place the chicken breasts back in the pain, nestling in the sauce, and cook until chicken is cooked through and sauce has thickened, 15-20 minutes.
Taste, adding salt and pepper as needed. Garnish with some extra thyme.
We like this served best over egg noodle in our house. But rice would do as well. The sauce is yummy, you just want something to soak up the flavor.