Preheat grill to approximately 400 degrees F.
Foil wrap sweet potatoes and place on grill while prepping remaining food.
Lay out 4 pieces of foil large enough to completely wrap each piece of salmon. Place 1 salmon fillet onto each piece of foil; add 1/2 tablespoon butter, a slice of lemon, and a sprinkling of dill to each (reserve remaining lemon for the veggies). Wrap up tightly and set aside.
Meanwhile, slice each zucchini in half crosswise and then quarter each section, making large chunks. Add to a mixing bowl with the mushrooms and season with 1 teaspoon of lemon zest, 1 teaspoon lemon juice, olive oil, salt, pepper, and grated Parmesan cheese. Toss well to coat evenly (feel free to use your hands!).
Place foil-wrapped salmon onto hot grill towards one side; place the veggies on the grill next to the salmon. Grill for 10 minutes or until fish is flakey and the veggies reach the desired tenderness. (Note: If veggies are not large enough to cook directly on grill, wrap them in foil before grilling). Using a potholder to protect your hand, gently squeeze potatoes to check for tenderness. Once done, remove from heat.
Serve each salmon fillet with half a potato, veggies, and sliced strawberries on the side.