Heat oil in a large skillet over medium-high heat. Season both sides of salmon fillets with salt and lemon pepper.
Add to hot skillet and cook until browned, about 2 minutes per side. Add vinegar to skillet and reduce heat to a simmer.
Continually spoon liquid over fish and cook until vinegar is thick and syrupy and salmon is cooked through, about 2 more minutes for medium, longer for well done. Serve immediately.