Combine oil, salt, and pepper in a bowl, stirring with a whisk. Combine butternut squash, parsnips, Brussels sprouts, and potatoes in a large bowl. Add oil mixture, garlic, and sliced lemon to vegetables; toss to coat.
Spread vegetable mixture in a single layer on a foil-lined baking sheet coated with cooking spray. Bake at 450°F for 35 minutes or until browned and tender, stirring gently with a spatula after 25 minutes. Remove pan from oven. Sprinkle vegetables with parsley, chives, dill, lemon zest strips, and lemon juice; toss.