Add the chicken, corn, potatoes, carrot, celery, onion, garlic, chicken stock, salt, and pepper to a slow cooker. If using fresh corn, add the corn cobs!
Cover and cook on high for 4 to 5 hours or low for 6 to 7.
Uncover and remove the chicken to a cutting board to shred.
Using an immersion blender, blend the soup for 5-10 seconds or until it is at your desired texture. You can remove some of the ingredients to have some texture left in the soup.
Add the chicken back to the soup along with the heavy cream and lemon juice, stirring until well combined. Cook another 10 to 15 minutes so all the flavors meld together.
Serve with parsley and more freshly cracked pepper and lemon juice if desired.