Stir the cumin, coriander, salt, pepper, allspice and nutmeg together in a small bowl to blend.
Put the lamb in a large bowl. Grate the onion on a box grater and add to the lamb. Add the spice mix. Blend well with your hands or a large fork and form into 4 patties.
Stir the feta and yogurt together in a bowl.
Toss the fennel in a bowl with the lemon juice, olive oil and ½ teaspoon salt.
Grill or broil the burgers until cooked to your liking. Serve the burgers on buns or pita, topped with some of the feta-yogurt sauce, fennel slaw, green sauce, lettuce, cucumber and sprouts.