Cook ground beef in a skillet over medium-high heat, stirring until it crumbles and is no longer pink. Drain and set aside.
Stir together ricotta cheese and 1 cup shredded Monterey Jack cheese.
Layer a lightly greased 13- x 9-inch baking dish with 3 egg roll wrappers and one-third each of ground beef, ricotta mixture, and beans; top with 1/2 cup salsa. Repeat layers twice with egg roll wrappers, beef, ricotta mixture, beans, and salsa. Top with remaining 3 egg roll wrappers and 2 cups salsa.
Bake at 350° for 40 minutes. Sprinkle with remaining 3/4 cup Monterey Jack cheese, and bake 10 more minutes or until cheese melts. Let stand 10 minutes before serving. Arrange avocado slices over lasagna.