Preheat the oven to 400°F (200°C).
Line a large sheet pan with parchment paper or lightly grease it with olive oil.
In a large bowl, toss the trimmed green beans with 1 tablespoon olive oil, minced garlic, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper until evenly coated.
Spread the green beans evenly on the prepared sheet pan.
Place the salmon fillets skin-side down on the sheet pan next to the green beans.
Brush the salmon fillets with the remaining 1 tablespoon olive oil.
Season the salmon with the remaining 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, and paprika.
Arrange lemon slices over and around the salmon fillets.
Place the sheet pan in the preheated oven and roast for 15 to 20 minutes, or until the salmon flakes easily with a fork and the green beans are tender-crisp.
Remove from the oven and let rest for 2 minutes before serving.