In large skillet, warm 1 tablespoon of oil over medium heat. Add chicken and brown on one side (about 5 minutes). Add remaining oil, turn chicken and brown well on second side, about 5 minutes longer. Transfer chicken to plate and set aside.

Coarsely chop onion. Add butter to skillet. Add onion and cook, stirring until soft (2 to 3 minutes).

Stir in the reserved flour and cook, stirring, until the flour is completely absorbed (about 1 minute).

Add the broth, 2 tablespoons lemon juice and thyme and bring mixture to a boil, stirring constantly.

Return chicken to skillet, reduce the heat to medium-low and cover the skillet. Cook until chicken is tender and opaque, about 5 minutes.

Remove chicken, stir remaining lemon juice into sauce in skillet and pour sauce over chicken. Sprinkle chopped parsley over all, if desired.