Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Cut the chicken breast into uniform 1-inch cubes and ensure the shrimp are peeled and deveined.
In a small bowl, whisk together the olive oil, minced garlic, dried oregano, dried thyme, sea salt, and black pepper.
Place the chicken cubes and broccoli florets in a large mixing bowl and drizzle with two-thirds of the herb oil mixture, tossing well to coat.
Spread the chicken and broccoli in a single layer on the prepared baking sheet.
Roast in the oven for 12 minutes.
While the chicken is roasting, toss the shrimp in the remaining herb oil mixture.
Remove the baking sheet from the oven, add the shrimp to the tray, and toss everything together briefly to combine.
Return the tray to the oven and roast for an additional 5 to 7 minutes, or until the chicken is cooked through and the shrimp are pink and opaque.
Remove from the oven, drizzle with fresh lemon juice, and serve immediately while hot.