Spray a skillet with cooking spray; heat over medium-high. Drop two eggs, separately, into hot skillet. This works best if you have egg molds to make a nice round shape, if not, simply babysit the eggs and continue to push them inwards while cooking, to keep them each fairly round. Be sure to cook through; once done, set them aside on a plate, covered. Continue until all eggs have been cooked.
Form the sausage into patties. In same skillet heat the sausage patties, browning each side. While they cook, mash the avocado and spritz with lime juice.
Assemble sandwich by placing sausage onto an egg, top with some mashed avocado and finally one more egg.