A leccarda is a drippings pan. Alla leccarda refers to a method of cooking on a spit (mostly game birds). Stuff the pigeons first with olives, then put the other ingredients (oil, garlic, capers, onions, olives, pancetta, whatever) into the leccarda and let them mingle with the drippings for basting.
It's a speciality of southern Umbria, where faraona (guinea fowl), or one of several words for wild pigeon (palombaccio, palomba colombaccio, picche or piccione alla leccarda) are very popular.
Image by latavolamarche