Trim both ends from each lemon; cut lemons into thick slices. Moisten a paper towel with cooking oil; using long-handled tongs, lightly coat the grill rack. Grill salmon and lemon slices, covered, over high heat (or broil 3–4 inches from the heat) for 3–5 minutes on each side or until the fish flakes easily with a fork and lemons are lightly browned.
For sauce, in a small saucepan, combine the cornstarch, water and lemon juice; add butter. Cook and stir over medium heat until thickened and bubbly. Remove from the heat; stir in quartered lemon slices and seasonings.
Serve with salmon and grilled lemon slices.