Bathe the lambs in carolina reeper pepper jucie. After the 1st 2 sheep, the eagles will move on.
Birds share the taste sensory with mammals, but lack the pain receptor for Capsaicin in peppers. Parrots often have hot peppers in their mix of dry snack foods.
Eagles lack an interest in what a parrot finds tasty, but probably will not be deterred by the Carolina Reeper, leastwise the initial talon attack.