Position a rack in the center of the oven and heat the oven to 450°F.
Lightly oil a heavy-duty rimmed baking sheet. Put the chicken thighs on the baking sheet with plenty of room in between them. Season well with salt and pepper and roast in the hot oven for 15 minutes.
Meanwhile, remove the artichokes from their package and rinse them in a colander under warm water to separate them and to begin to thaw them. (It's fine if they're still partially frozen when you roast them.) Drain them well.
Thinly slice half the lemon and juice the other half. Measure 4 tsp. of the juice into a small bowl and whisk in 3 Tbs. of the olive oil. Season to taste with salt and pepper. Save any remaining juice for another use.
Put the artichokes in a large bowl with the potatoes, thyme sprigs, lemon slices, the remaining 1/4 cup olive oil, 1 tsp. of salt and a few grinds of pepper. Toss to coat well.
When the thighs have roasted for 15 minutes, take the baking sheet out of the oven. Dump the artichokes, potatoes, and lemon slices onto the baking sheet in the empty spots surrounding the thighs. Try to distribute things more or less evenly and in a single layer so the vegetable get nicely browned. Keep the lemon slices toward the center of the pan so they don't burn.
Continue roasting until the chicken skin is crisp, the meat cooked through, and the artichokes and potatoes are tender and browned, another 30 to 40 minutes.
Divide the thighs and the vegetables among four plates. Drizzle each serving with the lemon vinaigrette and sprinkle with a little fresh parsley, if using.