In a large pot over medium heat, add the olive oil and butter. Once melted, add in the chopped celery, carrots, and onion. Stir for about 2 minutes, then add the garlic, cooking until slightly softened but not browned.
Deglaze the pot with white wine and let it cook down for a few minutes. Then, add in the chicken stock and water, bringing everything to a gentle bubble over medium heat.
Reduce the heat to low-medium and let the soup simmer for about 10 minutes, partially covered.
Break the lasagna noodles into smaller pieces and add them to the pot. Increase the heat to medium, stirring occasionally until the noodles are tender.
Once the noodles are cooked, turn off the heat. Add in the chopped celery leaves, lemon zest, and juice, followed by the heavy cream. Stir until everything is well-combined.
Add the shredded chicken, taste for seasoning, and adjust with salt and pepper as needed. Serve hot, garnished with fresh dill, chives, and black pepper.