Slice the bagel in half to create two circles. Remove some of the center of each slice to make a hole about 1 inch wide. Brush the sliced side of each half with olive oil.
Heat a skillet to medium-high heat and place the bagels sliced side down in the skillet when hot. Toast until golden brown. While the first side is toasting. combine the avocado and lemon juice. Flip the bagels in the pan so the sliced side faces up and spread the avocado onto each slice. Crack an egg into the center of each and season with salt and pepper.
Cover and reduce heat to medium. Cook until the egg is set, about 4 minutes for a soft yolk. Remove from the pan, serve, and enjoy!