Preheat oven to 425 degrees F. Line a large rimmed baking sheet with parchment paper or foil; coat with cooking spray.
Heat 1 Tbsp. oil in a large saucepan over medium heat. Add onion; cook, stirring often, until translucent, 3 to 5 minutes. Stir in garlic; cook for 1 minute. Stir in tomatoes, 1 Tbsp. dill, and 1/4 tsp. salt; bring to a boil over high heat. Stir in green beans. Reduce heat to low, cover, and simmer, stirring occasionally, until the beans are tender, 10 to 15 minutes.
Meanwhile, whisk lemon juice and the remaining 1 Tbsp. oil in a shallow bowl. Dip salmon in the lemon-oil mixture to coat well. Place the salmon, skin-side down, on the prepared baking sheet. Sprinkle with spice mix and the remaining 1/4 tsp. salt. Roast the salmon until it is just opaque in the center, about 10 minutes.
Divide the green bean mixture among 4 plates, add a piece of salmon, and sprinkle with the remaining 1 Tbsp. dill.
