Place salmon in a food processor and pulse until finely chopped. Transfer to a large bowl.
Add the minced onion, dill, honey, and horseradish to the salmon and mix.
Form into 4 patties. Season with salt and pepper and set aside.
Heat the oil in a 12 inch skillet on medium heat until shimmering. Add the patties and cooked until browned, about 2 minutes. Flip and cook until the burgers are cooked through.
Transfer to a paper towel lined tray and allow to rest for 2 minutes.
Divide lettuce and onion between the 4 bottom buns and place a salmon patty on top of each.