Preheat the oven to 400 degrees F. Apply a light coat of cooking spray to a large sheet pan.
Place the potatoes, carrots, parsnips, and fennel on a sheet pan and bake for 15 minutes.
Reduce the heat to 350 degrees F and add the cod to the oven. Do not remove the vegetables from the oven. Bake until the cod is cooked through and the vegetables are tender.
Meanwhile, heat the butter and lemon pepper seasoning in a small saucepan over low heat until the butter melts. Place the cooked vegetables in a large mixing bowl; sprinkle with the seasoned butter. Toss until vegetables are coated. Place the vegetables on a medium presentation platter and sprinkle with the fresh thyme leaves. Arrange the cod on top of the vegetables.