In a medium bowl, whisk together the lemonade, soy sauce, olive oil, ginger, brown sugar, garlic, lemon zest, 1/2 teaspoon salt and 1/4 teaspoon pepper.
Use a sharp knife to score the skin of the salmon, making three 1-inch incisions. Put the salmon and onions in a baking dish and pour the marinade over. Cover and refrigerate 1 hour, flipping halfway through.
Remove the salmon and onions from the marinade and discard the remaining liquid. Heat a nonstick grill pan over medium heat and drizzle with olive oil. Place the salmon on the pan skin-side down. Arrange the onion rounds and lemon slices in the pan around the fish.
Cook 3 to 5 minutes, then flip the fish, onions and lemons. Grill until the salmon is cooked through and the onions are soft and lightly charred, 5 to 8 minutes.
Place the salmon on a platter. Garnish with the grilled onions, lemon slices, lemon juice and parsley and sprinkle with salt and pepper.