In a bowl, mash the avocado with a fork until smooth. Mix in the lime juice. Season with salt and pepper to taste. Toast the bread and spread the avocado mixture on top.
Preheat a non-stick pan over medium low heat. Add the oil. Crack eggs on a flat surface and into the pan being careful not to break the yolk. Cook until the whites of the eggs start to become firm, add 1 to 2 tablespoons of water and cover with a lid to help firm the whites quicker. Season with salt and pepper.
Serve the eggs with avocado toast and apple. Garnish with red pepper flakes.