Preheat an outdoor grill for high heat and lightly oil the grate.
Grill salmon and thick lemon slices on hot grill until salmon flakes easily with a fork, 3 to 5 minutes per side.
Stir water, lemon juice, and cornstarch together in a small saucepan to dissolve the cornstarch; add butter and place over medium heat. Cook and stir the mixture until boiling and thick, 5 to 10 minutes. Remove saucepan from heat. Stir quartered lemon slices, dill, salt, chervil, and cayenne pepper into the sauce. Serve with the grilled salmon and grilled lemon slices.