Prepare a gas or charcoal grill for medium-high heat. Tear 4 pieces of heavy-duty aluminum foil into 12- to 14-inch squares.
Divide the potatoes among the 4 pieces of foil and arrange in the center in an area about the size of a salmon fillet. Sprinkle potatoes with paprika. Arrange green beans evenly over the potatoes. Lightly season with salt and pepper. Top beans with salmon fillets. Drizzle salmon with olive oil, sprinkle with thyme and season with salt and pepper, to taste.
For each packet, bring sides of foil up so edges meet and fold over at least twice until sealed, leaving room for steam. Pinch and seal foil ends.
Grill the packets 4 to 6 inches from heat on a covered grill 15 to 20 minutes or until salmon flakes easily with a fork. (Time depends on thickness of salmon.) To serve, place packets on dinner plates. Carefully snip to open foil and allow steam to escape. Use a spatula to remove food to plate or eat directly from foil. Squeeze lemon over salmon, if desired.
VARIATION: To make Baked Salmon Supper in Foil, prepare foil packets as recipe directs in Steps 2 and 3. Bake on a rimmed baking sheet in a preheated 400°F oven 20 to 25 minutes or until salmon flakes easily with a fork. (Time depends on thickness of salmon.)