Heat oven to 425°F. On rimmed baking sheet, toss broccoli and garlic with 1 Tbsp oil and 1/4 tsp each salt and pepper; roast 10 minutes.  Meanwhile, pound chicken breasts to even thickness, season with 1/4 tsp each salt and pepper, then coat in flour. Heat 1 Tbsp oil in large skillet on medium-high and cook chicken until golden brown,
 3 to 5 minutes per side. Nestle chicken amidst broccoli and roast until chicken is cooked through and broccoli is golden brown and tender, about 6 minutes. Return skillet to medium heat; add remaining Tbsp oil, then lemon pieces, and cook, stirring, until beginning to brown, 3 minutes. Add lemon juice and 1/3 cup water and cook, stirring and scraping up any browned bits. Spoon over chicken and serve with broccoli.