Spring is lazy in the Adirondacks. We have pockets of snow some years as late as June. The one way I can remind myself that spring has in fact sprung is by using seasonal ingredients—even if they're grown somewhere else.
In a medium bowl, season the lamb and spring onions with kosher salt and pepper. Mix in the fresh herbs and about 1 tbsp. oil. Form into 4 patties (thinner in the centers for even cooking). Refrigerate for 1 hour
In a small bowl, cover the sun-dried tomatoes with very hot water. Let stand until softened, 10 to 20 minutes. Drain and thinly slice the tomatoes.
In a small skillet, toast the walnuts over medium heat, stirring occasionally, until fragrant and toasted, about 5 minutes. Let stand until cool, about 5 minutes. In a food processor, pulse the nuts just until finely chopped (but not to a paste). Add the feta, half the lemon juice, the garlic, dried oregano, and a drizzle of oil. With the machine running, gradually stream in the milk until a thick sauce forms. Season the feta-walnut sauce.
Heat a cast-iron skillet over medium-high. Add the patties. Cook, turning occasionally, for about 6 minutes for pink centers or about 8 minutes for medium-well. Douse the patties with the remaining lemon juice.
Place the burgers on the roll bottoms. Top with the sun-dried tomatoes and lettuce. Slather a layer of the feta-walnut sauce on the roll tops and set in place.