Preheat oil to 325 degrees F.
Remove leaves from the rosemary 5 inches from base of stem to make skewers. Whip the eggs in a small bowl. In a another bowl, combine the flour, Cajun seasoning, salt, and freshly ground black pepper. On each skewer, place 2 shrimp, 1-ounce lobster meat, and 2 shrimp. Repeat this for all skewers. Roll each skewer in seasoned flour, then egg, then flour again and repeat this on each skewer twice, making sure to only coat the lobster and shrimp. Check temperature on oil and begin frying. Fry each skewer for 4 to 5 minutes or until batter is golden brown. Serve.