In a small skillet, toast the pistachios over medium until fragrant and browned, about 5 minutes; let cool. Transfer to a food processor; pulse to a coarse dust. Transfer to a small bowl. In a strainer, salt the cucumber. Let drain 15 minutes, then pat dry. In the food processor, finely chop the mint, parsley and dill. Add the cucumber, yogurt, feta, lemon juice, garlic and cumin; process into a chunky sauce. Season with salt and transfer to a serving bowl. Stir in the pistachios.
In a bowl, combine the lamb, wine, garlic, cumin, oregano, paprika, allspice and a drizzle of oil; season with kosher salt and black pepper. Form into 8 small patties (thinner in the center for even cooking).
Heat a skillet over medium-high. Add the lamb patties and cook, turning once, until browned, 6 to 7 minutes for medium.
Serve the lamb patties with the pita, lettuce, vegetables and tzatziki.