Place the scallions and celery in a bowl of cold water (they will curl). In a separate small bowl, season the yogurt to taste with salt and pepper and stir to combine.
In a large bowl, combine the lamb and za’atar. Grate the garlic into the bowl along with 2 teaspoons jalapeño. Thinly slice any remaining jalapeño and set aside.
Season the lamb with salt and pepper, then mix thoroughly with your hands to combine. Form the lamb mixture into 8 patties and place on a plate or clean cutting board.
In a large skillet, heat 2 tablespoons oil over medium-high. Sear the patties until browned on the outside and cooked to medium, about 4 minutes per side.
Drain the scallions and celery, pat dry, and place in a separate medium bowl. Add the cucumbers and sliced jalapeño. Squeeze about 2 teaspoons lemon juice over the vegetables (or more as needed to coat), then season with salt and pepper.
Serve the lamb patties with the yogurt and salad. Sprinkle additional za’atar over the salad and yogurt if desired.