Lay out two large pieces of tin foil. Divide the asparagus between each and top with a piece of salmon. Sprinkle the dill over each. Place the butter and a lemon slice on each piece of salmon. Place the tomatoes around the salmon and sprinkle the salt over everything. Fold the tin foil into a packet leaving space around the salmon inside so the air can circulate.
Once the grill is preheated, turn off one set of burners. Place the packets on those burners and close the lid. Let them cook for 8-10 minutes. Carefully remove them from the grill, unfold them, and serve.