Cook pasta according to package directions, omitting salt and fat. Drain, reserving 1 cup cooking water.
While pasta cooks, stir together parsley, 1 tablespoon of the oil, 1 1/2 tablespoons of the lemon juice, and 1 tablespoon of the capers in a small bowl. Set aside.
Heat a large nonstick skillet over medium-high. Lightly coat salmon with cooking spray, and sprinkle with pepper. Add salmon to skillet; cook until fish is golden brown and flakes easily with a fork, 3 to 4 minutes per side, or to desired degree of doneness. Remove from heat; transfer salmon to a plate. Wipe skillet clean.
Reduce heat to low, and add remaining 2 tablespoons oil to skillet, garlic, and lemon zest. Cook, stirring often, until garlic is golden brown in spots, about 2 minutes. Stir in pasta, salt, and reserved cooking water. Increase heat to medium-high; and cook, stirring or shaking skillet constantly, until pasta has absorbed most of the liquid and a thin sauce clings to pasta, 2 to 4 minutes. Remove from heat, and stir in remaining 1 1/2 tablespoons lemon juice and 3 tablespoons capers. Divide pasta evenly among 4 plates. Spoon parsley mixture evenly over fish, and flake fish into large chunks. Top each pasta serving with salmon-parsley mixture; serve with lemon slices.