Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Slice the summer squash into half-moons and dice the chicken breast into uniform 1-inch cubes.
In a large mixing bowl, combine the chicken, squash, olive oil, minced garlic, dried thyme, sea salt, and black pepper.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the oil and seasonings.
Spread the mixture in a single layer on the prepared baking sheet, ensuring the pieces are not overcrowded to allow for proper browning.
Roast in the center of the oven for 18 to 20 minutes, or until the chicken is cooked through and the squash is tender and golden.
Remove from the oven and immediately sprinkle with the grated parmesan cheese and fresh chopped parsley.
Drizzle the fresh lemon juice over the entire tray before serving to brighten all the flavors.