Heat oven to 400 degrees. Lightly season fish on both sides with salt and pepper.
Cut four pieces of parchment paper, each measuring 12 by 17 inches, and lay them on a clean work surface. Fold each in half crosswise, then open and lay flat.
Divide spinach leaves among parchment, mounding on one side of the fold. Divide butter in half, then divide one of the halves among the four papers, spooning it on top of spinach; top each with 2 lemon slices. Lay a fillet on top of the lemons and spoon remaining butter on fish. Fold over parchment and form a half-moon packet, beginning at one corner; make small overlapping pleats all the way around to seal the edges completely.
Transfer packets to a rimmed baking sheet and cook until parchment puffs up, about 12 minutes (8 minutes per inch of thickness for firm-fleshed fish).
Immediately place a packet on each of four plates and use kitchen shears to cut open the packets at the table. Serve with lemon wedges.