Preheat the oven to 425°F and line a large sheet pan with parchment paper or foil for easy cleanup.
Place the halved potatoes in a large bowl and toss with 1 tablespoon olive oil, half the minced garlic, half the lemon zest, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 teaspoon thyme until evenly coated.
Spread the potatoes in a single layer on the sheet pan and roast for 15 minutes so they begin to soften and brown.
While the potatoes roast, add the chicken thighs to the same bowl and toss with the remaining olive oil, garlic, lemon zest, salt, pepper, and thyme.
Remove the pan from the oven, nestle the chicken thighs among the potatoes, and return the pan to the oven for 15 minutes.
Add the asparagus to the pan and drizzle with half the lemon juice. Toss gently to coat, then roast for 10 to 12 more minutes until the chicken reaches 165°F and the asparagus is crisp-tender.
Remove the pan from the oven, drizzle with the remaining lemon juice, and sprinkle with chopped parsley before serving.