Using spiralizer, cut zucchini into ⅛-inch-thick noodles, then cut noodles into 12-inch lengths. (You should have 2 pounds zucchini noodles after spiralizing; reserve any extra noodles for another use.)
Adjust oven rack to middle position and heat oven to 375 degrees. Toss zucchini noodles with 1 tablespoon oil and salt on rimmed baking sheet and spread into even layer. Roast until zucchini is tender, 20 to 25 minutes. Transfer zucchini to colander and shake to remove any excess liquid.
Meanwhile, heat remaining 2 tablespoons oil, garlic, pepper flakes, and thyme in 12-inch nonstick skillet over medium heat, stirring occasionally, until garlic is fragrant and just beginning to brown at edges, 3 to 5 minutes. Add clam juice and bring to simmer. Add shrimp, cover, and cook, stirring occasionally, until just opaque, 3 to 5 minutes. Off heat, transfer shrimp to bowl using slotted spoon and cover to keep warm.
Return sauce to simmer over medium-high heat and cook until reduced to ½ cup, about 5 minutes. Off heat, whisk in butter, 1 piece at a time, until combined. Whisk in lemon juice and parsley and season with salt and pepper to taste. Add shrimp and any accumulated juices and zucchini and gently toss to coat. Serve.