Boil the chicken in a pan with enough water to cover it for about 45 minutes (you can top up with water to ensure proper coverage during boiling). Take the chicken out and let it cool down slightly. Once cooled, tear the meat into shreds with your hands; alternatively, use a knife to cut the chicken into medium-size pieces. Optional: To avoid clumps of unappetizing blood in the soup, you can pass the chicken broth through a fine colander, and then wash the saucepan well to scrape any blood residue from the bottom.
Once the chicken is cut/shredded, the broth is blood-free and the pan is clean, put the meat and broth back into the pan and return to boil under medium heat. Add lemon juice, oregano, thyme and bay leaves, as well as all of the vegetables except for the spinach.
Once the vegetables are nearly cooked (about 15 minutes after they were added to the pan), add orzo. Let the soup simmer for 8-10 minutes under medium heat, mixing frequently with a wooden spoon to avoid the pasta sticking to the bottom of the pan. Add warm water if soup is too thick and/or chunky. Lastly, add spinach and let it wilt slightly. Add salt and pepper to taste and extra lemon juice, if desired. Take the soup off the heat a couple of minutes after adding the spinach. Serve hot.