Preheat oven to 425 degrees F. Take 4 sheets of parchment paper, each about 12 by 16 inches, in half and then unfold to make a crease. Place a pile of sweet potato strips on one side of each piece of parchment and top each with a piece of cod. Sprinkle each piece of fish with 1 teaspoon of matcha, then top each with 1 tablespoon butter, 2 sprigs thyme and a slice of lemon; season with salt.
Fold over parchment paper to enclose filling and crimp edges to seal and form a crescent-shaped packet. Transfer to a baking sheet and bake for 20 minutes. Remove packets from oven and allow to rest for 5 to 10 minutes before opening.