Prepare the skewers: If using bamboo skewers, soak them in water for 1 hour to prevent burning. Metal skewers do not require soaking.
Heat the grill: Preheat your grill over medium heat and spray the grates with oil to prevent sticking.
Season the salmon: Place the salmon chunks in a large bowl and lightly spritz them with olive oil spray. In a separate small bowl, mix the sweet paprika, cayenne pepper, garlic powder, thyme, oregano, kosher salt, and black pepper. Rub the spice blend evenly over the salmon pieces.
Prep the lemons: Cut one lemon into wedges for serving. Slice the remaining two lemons into thin rounds.
Assemble the skewers: Thread the salmon chunks and folded lemon slices onto pairs of skewers, alternating between the two. This makes 8 skewers total.
Grill the skewers: Lightly spray the assembled skewers with olive oil spray to ensure they don't stick to the grill grates. Grill for 8-10 minutes, turning occasionally, until the salmon is opaque and slightly charred.
Serve: Transfer the skewers onto a platter, sprinkle with chopped parsley, and serve with lemon wedges alongside.