In a large mixing bowl, combine the salmon, rolled oats, onion, egg, lemon juice, Dijon mustard, salt, and pepper. Stir until the ingredients are evenly mixed and hold together without being overly wet.

Divide the mixture into four equal portions. Shape each portion into a patty about 1 inch thick.

Heat a large skillet over medium-high heat and add the vegetable oil. Once the oil is shimmering, carefully place the salmon patties into the skillet.

Pan-fry each patty for about 7 minutes on the first side until golden brown and crisp. Flip, then cook for another 7 minutes on the other side. The patties should be cooked through and slightly firm to the touch.

Remove the patties from the skillet and serve hot. Pair with your favorite burger buns, lettuce, and toppings, or enjoy alongside a fresh salad!