Preheat oven to 350 degrees F (175 degrees C). Arrange aluminum foil on a work surface and lightly spray cooking spray onto 1 side of each.
Place 1 swai fish fillet onto the middle of each piece of foil; season with salt and pepper. Layer lemon slices, mushroom slices, onion slices, and capers onto each swai fillet. Fold foil over each swai fillet creating a packet. Place packets on a baking sheet.
Bake in the preheated oven until fish flakes easily with a fork, about 15 minutes.