Preheat the oven to 425°F (220°C).
In a large bowl, toss the halved baby potatoes with 1 tablespoon of olive oil, 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Spread the potatoes evenly on a large sheet pan and roast in the preheated oven for 10 minutes.
While the potatoes roast, in the same large bowl, combine the shrimp, green beans, minced garlic, smoked paprika, remaining 2 tablespoons olive oil, and remaining 1/2 teaspoon salt. Toss to coat evenly.
After the potatoes have roasted for 10 minutes, remove the sheet pan from the oven and add the shrimp and green bean mixture evenly over the potatoes.
Arrange the lemon slices on top of the shrimp and vegetables.
Return the sheet pan to the oven and roast for an additional 10 minutes, or until the shrimp are pink and opaque and the green beans are tender-crisp.
Remove from the oven and sprinkle with chopped fresh parsley before serving.