Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes, then toss them on the baking sheet with half of the olive oil and a pinch of salt and pepper.
Spread the potatoes in a single layer and roast for 10 minutes.
While potatoes roast, mince the garlic and finely chop the fresh rosemary and thyme.
In a small bowl, combine the remaining olive oil, minced garlic, rosemary, thyme, salt, and pepper to create a herb paste.
Pat the chicken breast dry and rub the herb paste evenly over all sides.
Remove the baking sheet from the oven, move the potatoes to one side, and place the chicken and broccoli florets on the other side.
Return the sheet to the oven and roast for 18 to 22 minutes, or until the chicken reaches an internal temperature of 165°F.
Drizzle the fresh lemon juice over the chicken and broccoli before serving hot.