Prepare a grill for medium-high heat.
Toss the onion, lemon and garlic with a generous pinch each of salt and pepper. Spread the mixture in the center of a 24-inch-long piece of heavy-duty foil. Put the salmon on top of the onion mixture, drizzle with the butter and sprinkle with the Italian seasoning and a generous amount of salt and pepper. Bring the 2 long sides of foil together and fold over twice to seal. Bring the ends of the foil in and crimp to seal, leaving a bit of room for steam to circulate inside.
Place the packet on the grill and cook for 10 to 15 minutes. Careful of the steam, open the packet and check the salmon. It should be mostly opaque with a slightly rosy center. Transfer the package to a cutting board and set aside for about 5 minutes.
Cut the salmon into 4 equal pieces and transfer to 4 plates. Evenly spoon the onions, lemons and collected juices over the salmon.
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