Preheat oven to 400°F (200°C).
Line a large rimmed baking sheet with parchment paper or aluminum foil for easy cleanup.
Place the carrot sticks on the baking sheet, drizzle with 1 tablespoon of olive oil, and season with half of the salt, pepper, and garlic powder.
Roast carrots in the preheated oven for 10 minutes, as they require longer cooking time than the asparagus.
Remove the tray from the oven and add the asparagus spears to the sheet.
Drizzle the asparagus with the remaining 1 tablespoon of olive oil and the rest of the seasonings, tossing all vegetables together to coat evenly.
Return the baking sheet to the oven and roast for an additional 10 to 12 minutes, or until the asparagus is tender and the carrots are slightly caramelized.
Drizzle with fresh lemon juice immediately before serving.