Preheat your frying pan on medium-low heat. Cut the avocado in half and scoop the puree out into a small bowl. Add lemon juice, salt, and pepper to mashed avocado and mix.
Spread mayonnaise on the outside of each slice of bread. Spread avocado mix onto the bread (not the mayo side), top with cheese, and another bread slice (mayo side up).
Add some butter to the pan, then place the sandwich onto it and fry until browns. Flip and fry until browns on the other side as well.
While the sandwich is frying make all the rest of the sandwiches. Fry all of them like you did with the first one.
Enjoy! Serve on the side of a tomato soup or with your favorite dipping sauce!