Lemon Chicken Soup With Orzo

I got this recipe from an Ellie Krieger cookbook, and as the weather has actually cooled off here in Houston I thought it was perfect timing to make a big batch of soup.
I think this soup turned out yummy, although it was a tad too lemony so next time I think I'll cut the amount of lemon juice in half.

4 teaspoons olive oil
8 ounces chicken breast cut into small chunks
Pinch of salt, plus more to taste
1 medium onion, diced (about 1 1/2 cups)
2 stalks celery, diced (about 1/2 cup)
1 medium carrot, diced (about 1/2 cup) (I didn't have any carrots so left it out)
2 teaspoons chopped fresh thyme or 1/2 teaspoon dried
6 cups low-sodium chicken broth
1 cup orzo
2 large eggs
3 tablespoons fresh lemon juice
Freshly ground black pepper to taste

Heat 2 teaspoons of the oil in a soup pot over medium-high heat. Season the chicken with the salt, add it to the pot, and cook, stirring, a few times, until just cooked through, about 5 minutes. Transfer the chicken to a dish and set aside.
Add the remaining 2 teaspoons oil to the pot. Add the onion, celery, carrot, and thyme and cook, stirring over medium-high heat until the vegetables are tender, about 5 minutes. Add 5 cups of the broth and bring to a boil. Add the orzo and let simmer until tender, about 8 minutes. Turn the heat down to low to keep the soup hot but not boiling. Warm the remaining 1 cup broth in a small saucepan until it is hot but not boiling. In a medium bowl, beat the eggs. Gradually whisk the lemon juice into the eggs. Then gradually add the hot broth to the egg-lemon mixture, whisking all the while. Add the mixture to the soup, stirring well until the soup is thickened. Do not let the soup come to a boil. Add the cooked chicken to the soup.