Pat the salmon dry. Roughly chop two-thirds into small 1/4-inch pieces for texture. Add the remaining one-third to a food processor and pulse until it forms a sticky paste.
In a large bowl, combine the chopped salmon, salmon paste, panko, egg, Dijon, scallions/onion, garlic, smoked paprika, lemon zest, 1 tablespoon lemon juice, salt, and pepper. Stir until just combined. Don't overmix.
Divide into 4–6 patties (about 1/2 to 3/4 inch thick). Place on a parchment-lined tray and chill for 20–30 minutes. This step is clutch for cohesion.
In a small bowl, whisk Greek yogurt, mayo, remaining lemon juice, chopped dill, a pinch of salt, and pepper. Taste and adjust—more lemon for tang, more dill for pop. Chill until serving.
Heat a skillet or grill pan over medium. Lightly oil or butter the cut sides and toast until golden. Set aside.
Heat 1–2 tablespoons oil in a large nonstick or cast-iron skillet over medium to medium-high. Add patties and sear 3–4 minutes per side, until deeply golden and cooked to 125–130°F in the center for medium (carryover will finish it). Don't move them too early—let the crust form.
Spread dill sauce on both buns. Add lettuce, patty, tomato, pickles, and a sprinkle of fresh dill if you're feeling fancy.
Finish with a squeeze of lemon. Yes, on a burger. It slaps.