Add the chicken, corn, potatoes, carrot, celery, onion, garlic, stock, and salt to a 6-quart slow cooker.
Cover and cook on high for 4-5 hours, or low for 6-7, or until the vegetables are tender and the chicken is cooked through and easily shreddable with a fork. Do not uncover during this time.
Uncover and remove the chicken to a cutting board. Using an immersion blender, blend the soup for 5-10 seconds. Alternatively, carefully, remove ½ to 1 cup of the vegetable and broth mixture to a blender. Cover, blend on high, then add back to the soup, stirring to combine. Note: Blending for just a few seconds will add a natural creaminess to the soup, while leaving the texture of most of the vegetables.
Add the cream cheese to a medium bowl. Ladle in a few tablespoons of the hot soup, whisking to combine. Pour the cream cheese mixture into the soup.
Shred or dice the chicken. Add the chicken back to the soup along with the lemon juice, stirring until the cream cheese is well combined.
Taste and add additional salt or lemon juice if desired. Serve with parsley and freshly cracked pepper if desired.
