Stir together vinegar, water, lemon juice, and brown sugar in a small bowl.
Pat salmon dry and season with salt and pepper. Heat oil in a 12-inch nonstick skillet over moderately high heat but not smoking. Increase heat to high, add salmon skin side up, and sear until well browned, about 4 minutes. Turn fish over and sear until just cooked through, 3 to 4 minutes more.
Transfer salmon to plates and carefully add vinegar mixture to skillet (liquid will bubble vigorously and steam). Simmer, stirring, until thickened and reduced to about 1/3 cup, about 2 minutes. Spoon glaze over salmon.