Preheat oven to 425°F. Prepare four parchment hearts.
Arrange a fish fillet over half of each heart. Season with salt and pepper.
Divide artichokes, tomatoes, olives, capers, and garlic over and around each fish fillet. Top each with 2 thyme sprigs. Drizzle each fillet with 1 tsp. lemon juice and 1/2 Tbs. olive oil. Seal packages.
Arrange packets on two large baking sheets. Bake 8 to 10 minutes, depending on fillet thickness, switching pan position halfway through. Transfer the packets to plates with a wide spatula. Slit tops; gently open. Serve with orzo.