In a large skillet, heat olive oil over medium heat. Sauté carrots, celery and onions in hot oil until vegetables begin to soften. Add garlic; cook and stir until fragrant, about 1 minute. Transfer mixture to slow cooker.
Add thyme, oregano, 1 teaspoon salt, 1/2 teaspoon pepper, bay leaf, chicken broth, and chicken to slow cooker; stir.
Cover and cook on low 6 - 7 hours or on high 3 - 4 hours.
Remove bay leaf and chicken. Shred chicken and return to slow cooker.
Cook pasta according to package directions. While pasta is cooking, squeeze lemons for juice and zest.
Add cooked pasta, lemon juice, zest and baby spinach to slow cooker. Cover and cook on low about 5 minutes or until spinach wilts into the broth.
Ladle into bowls and top with Parmesan cheese, if desired.