Lay out 1 large sheet (about 16 inches by 12 inches) of parchment paper. Place 4 of the asparagus spears in the center of the paper, then 1 fish fillet on top and then a slice of lemon. Season with salt and pepper, 1 tablespoon of the lemon juice, 1 tablespoon of the olive oil and 1 sprig of the thyme. Fold over the ends of the parchment to enclose the fish. Place on a rimmed baking sheet. Repeat with the remaining ingredients.
Bake for 12 to 15 minutes, or until the fish reaches 130 to 135 degrees F on a thermometer.