In a large pot, heat 2 tablespoons olive oil over medium heat. Add 1 diced onion, the carrots, celery, and the minced garlic; season with salt and pepper. Cook, stirring occasionally, until the vegetables begin to soften (about 3-5 minutes).
Add chicken broth, water, bay leaf, and thyme. Bring to a boil; reduce heat to low, cover, and simmer until vegetables are tender (about 20 minutes). Stir in cooked chicken, orzo, and the juice from the remaining lemon. Simmer, uncovered, until the orzo is tender (about 10-12 minutes). Stir occasionally so that the orzo doesn’t stick.
Remove bay leaf. Season soup with salt and pepper, to taste. Stir in fresh dill and add extra chicken broth to thin, as necessary.
Serve immediately, or allow to cool completely before storing in an airtight container in the refrigerator for up to 3 days (or in the freezer for up to 3 months).