Toast the pumpernickel bread slices until they are crisp and firm.
Cut the avocados in half, remove the pits, and scoop the flesh into a bowl. Add the lemon juice, salt, and black pepper, then mash with a fork until mostly smooth with some small chunks remaining.
Spread the mashed avocado evenly over each slice of toasted bread.
Heat a skillet over medium heat and crack the eggs into the pan. Cook until the whites are set but the yolks are still runny, about 3 to 4 minutes.
Place one fried egg on top of each avocado toast. Arrange the sliced black olives on the avocado to form simple cat features such as ears and whiskers.