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Preheat oven to 425 degrees F. Line a large rimmed baking sheet with parchment paper or foil; coat with cooking spray.
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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.
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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.
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Divide the green bean mixture among 4 plates, add a piece of salmon, and sprinkle with the remaining 1 Tbsp. dill.
