First of all, toast the fennel seeds... Heat a small, ungreased sauté pan over high heat. Once warm, place the fennel seeds in the pan and agitate the pan briskly back and forth to prevent the seeds from sticking to the bottom and burning. (You can use a wooden spoon to constantly stir the seeds if you prefer). Cook the fennel seeds for 3 to 4 minutes, or until they become fragrant and slightly darker brown. Remove from the heat and place the seeds in a small bowl or scattered on a baking sheet to cool. When cool, roughly crush them in a pestle and mortar, or with a rolling pin.
Squeeze the juice from the lime. Rub the lamb with a little oil and half the lime juice, then season with salt and freshly ground black pepper. Barbecue or cook in a hot griddle pan (broiler pan) for 10-15 minutes, turning occasionally. Remove from the heat, cover with aluminium foil and set aside to rest and keep warm. (If you are using left-over lamb, you can simply reheat in a microwave)
Meanwhile, in a large bowl, whisk the remaining lime juice, a little olive oil and the fennel seeds together with salt and freshly-ground black paper to your taste. Peel and grate the carrot and peel and finely chop the red onion. Add them to the bowl and mix well.
Warm the pitta breads on the barbecue or griddle pan, then make a slit in each to form a pocket. Slice the lamb and stuff into the pittas with the carrot salad and lettuce leaves (Little Gem lettuces are perfect for this). Eat while still warm.