Preheat Oven: Preheat the oven to 425°F. Line a rimmed baking sheet with aluminum foil.
Dress Salmon: Place the salmon fillets on a plate. Spoon 2 tablespoons of lemon dressing over each fillet, using ¼ cup total. Spread the dressing evenly over the salmon and set it aside.
Slice Potatoes: Cut the red potatoes into thin, even rounds so they cook at the same rate.
Prepare Thyme: Remove the thyme leaves from the stems and finely chop them.
Season Vegetables: Place the sliced potatoes and grape tomatoes in a large mixing bowl. Add the chopped thyme, 3 tablespoons of lemon dressing, kosher salt, and black pepper.
Toss Vegetables: Toss the potatoes and tomatoes until they are evenly coated with the dressing and seasonings.
Arrange Vegetables: Spread the potato and tomato mixture in a single layer on the prepared baking sheet.
Roast Vegetables: Roast the vegetables for 20 minutes, or until the potatoes begin to soften and the tomatoes start to blister.
Add Salmon: Remove the baking sheet from the oven. Carefully move the vegetables toward one side of the pan and place the dressed salmon fillets on the open side.
Bake Salmon: Return the baking sheet to the oven. Bake for 10 to 12 minutes, or until the salmon flakes easily with a fork and reaches 145°F in the thickest part.
Plate Salmon and Potatoes: Transfer the cooked salmon and roasted potato slices to serving plates. Leave the roasted tomatoes and their juices on the baking sheet.
Blend Tomato Sauce: Transfer the roasted tomatoes and their juices to a food processor. Add the salted butter and blend until the mixture is smooth and creamy.
Sauce Salmon: Spoon the warm tomato-butter sauce over the baked salmon.
Prepare Garlic: Finely mince the garlic cloves if they have not already been prepared.
Heat Dressing: Place a large skillet over medium heat. Add the remaining 1 tablespoon of lemon dressing and warm it for about 30 seconds.
Sauté Garlic: Add the minced garlic and crushed red pepper. Cook for about 30 seconds, stirring constantly, until fragrant.
Cook Vegetables: Add the sliced onion, zucchini, and yellow squash. Increase the heat to medium-high and cook for 5 to 7 minutes, stirring often, until the vegetables are tender but not mushy.
Prepare Arugula: Place the fresh arugula in a large serving bowl.
Make Warm Salad: Pour the hot onion and squash mixture over the arugula. Toss gently until the arugula softens slightly from the heat.
Serve Dinner: Serve the warm vegetable salad alongside the salmon, lemon potatoes, and buttery tomato sauce.