Heat the oil in a large saucepan over medium heat. Add the onions and season lightly with salt and pepper. Sauté until the onions are translucent.
Add the broth and bay leaf and bring to a simmer. Add the chicken and cauliflower rice. Simmer for 10 minutes or until the cauliflower rice is just tender.
In a medium bowl, whisk together the lemon juice and egg. Slowly ladle 1 cup of hot broth from the soup into the lemon-egg mixture, stirring until combined. Then slowly pour the lemon-egg mixture into the saucepan, slowly whisking until combined.
Discard the bay leaf. Serve with lemon slices and chopped fresh parsley.