Heat a heavy-bottomed pot over medium heat and add a splash of olive oil until it shimmers and begins to lightly smoke.
Add chopped onion, carrots, and celery to the pot. Sauté, stirring occasionally, until the vegetables are tender and fragrant, about 8 minutes. They should be soft and slightly translucent.
Toss in shredded cooked chicken, stirring to combine, and let it warm through for about a minute. The mixture will smell savory and inviting.
Pour in the chicken broth, bringing the mixture to a gentle simmer. Once bubbling, add thyme and bay leaves, then reduce the heat to low and let the soup simmer uncovered for 20-30 minutes, allowing the flavors to meld and the broth to deepen in color.
Taste the broth and season with salt and pepper as needed. Remove the bay leaves and thyme sprigs if used fresh, and discard.
Zest the lemon into the soup and squeeze in some juice for brightness. Stir gently to combine, giving the broth a fresh, tangy kick.
Serve the soup hot, ladled into bowls. The broth should be clear and golden, with tender vegetables and flavorful shredded chicken, ready to enjoy as a comforting, customizable meal.