Preheat the oven to 425°F (220°C). Line a large sheet pan with parchment paper or lightly grease it.
In a large bowl, combine the sliced yellow squash and zucchini with 2 tablespoons of olive oil, half of the minced garlic, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and the dried Italian seasoning. Toss until the vegetables are evenly coated.
Spread the seasoned squash and zucchini in a single layer on the prepared sheet pan.
Roast the vegetables in the preheated oven for 10 minutes.
While the vegetables roast, in the same bowl, combine the shrimp with 1 tablespoon olive oil, the remaining minced garlic, smoked paprika, and a pinch of salt and pepper. Toss to coat evenly.
After the vegetables have roasted for 10 minutes, remove the sheet pan from the oven and add the shrimp in a single layer on top of the vegetables.
Return the sheet pan to the oven and roast for an additional 5 to 7 minutes, or until the shrimp are pink and opaque and the vegetables are tender.
Remove the sheet pan from the oven. Drizzle the fresh lemon juice over the shrimp and vegetables and sprinkle with chopped fresh parsley.
Gently toss everything on the sheet pan to combine flavors before serving.