Heat olive oil in a large Dutch oven or soup pot over medium-high heat. When hot, add minced garlic and cook, stirring often, until fragrant.
Pour in chicken stock, then add skinless chicken thighs, white rice, and bay leaves. Bring to a boil, then reduce heat to medium-low to medium. Simmer until chicken is fully cooked and the rice is tender.
Remove the bay leaves and discard. Transfer the cooked chicken thighs to the bowl of a stand mixer with beater attached, then beat on medium speed until chicken is fully shredded.
Drizzle and whisk the tempered egg and lemon mixture back into the chicken soup slowly.
Bring the heat back up to medium to medium-high, then cook to thicken. Taste and adjust seasoning.