Eggs and breadcrumbs are added to traditional Greek Burgers because they are an adaptation of Greek meatballs, plus they make for extra juicy burgers!  The breadcrumbs serve three purposes:  1) help bind the ingredients together so the lamb burgers don’t fall apart, 2) add structure to allow you to add additional liquid to produce moister/more flavorful burgers and 3) help the burgers stay moist by absorbing and trapping the meat juices as they cook. The eggs bind the ground meat, breadcrumbs, and herbs together. As the patties cook, the eggs cook which helps all the ingredients stick together instead of crumble apart.