Preheat your oven to 220°C (430°F) and line a baking sheet with parchment paper.
Peel the carrots if they have thick or pale skin, then cut them into uniform sticks about 2-3 inches long.
Trim the woody ends off the asparagus, and if the spears are thick, lightly peel the bottom third for even roasting.
Place the carrots and asparagus in a large bowl, then drizzle with about 3 tablespoons of olive oil, tossing well to coat all pieces evenly.
Sprinkle generously with coarse sea salt and freshly cracked black pepper, then toss again to distribute evenly.
Spread the vegetables out in a single layer on the prepared baking sheet, keeping the carrots and asparagus separate if you prefer easier checking.
Roast in the oven for 20-25 minutes, tossing halfway through, until the carrots are caramelized and tender, and the asparagus tips are smoky and crisp.
Once roasted, remove from the oven and squeeze fresh lemon juice over the vegetables to brighten their flavors.
Give everything a gentle toss to combine the flavors and serve immediately while warm, optionally garnished with extra herbs or a drizzle of olive oil.