Cut the chicken into small-medium chunks. In a plastic or paper bag, mix flour, salt and pepper; shake to mix. Add chicken into the bag and shake lightly to coat. Remove the chicken and reserve the excess flour.
In a large skillet, warm 1 tablespoon of oil over medium heat. Add chicken and brown on one side for about 3 to 5 minutes. Add the remaining tablespoon of oil and flip the chicken over. Once the other side has browned for about 3 to 5 minutes, transfer the chicken to a plate; put it aside.
Add butter to the skillet, then add in the diced onion. Cook until softened and slightly translucent, about 2 minutes. Stir in reserved flour and cook, while stirring, for one minute. Add in the chicken broth and lemon juice. Bring the mixture to a boil, stirring constantly. Return the chicken to the skillet and cook until tender, about 5 minutes. Remove from heat and serve immediately.