Add the chicken breasts to the bottom of a slow cooker. Sprinkle the chicken breasts with salt and pepper to taste. Spread pesto over the chicken, then squeezes on the lemon juice.
Cut the butter into slices and place over the chicken. Cover and cook on low for 5-6 hours. Near the end of the cooking time, cook the pasta according to package directions. Drain well.
Shred the chicken in the crockpot using 2 forks. Add the cooked pasta and the parmesan cheese, stir until everything is coated with the buttery pesto sauce and the chicken is mixed well into the pasta.
Add the mozzarella cheese in the crockpot over the pasta. Cover and cook for 15 minutes more or until the cheese has melted.