To a large pot, add 1 tbsp olive oil, onion and lemon strips.
Allow to sweat for 7 minutes over low-medium heat while covered. Make sure that no color develops.
Add chicken stock or broth to the pot along with the rice, bay leaf and bring to a boil over medium heat. Reduce heat to and simmer until rice is tender and stock is aromatic, about 20 minutes.
With slotted spoon, remove and discard bay leaf and lemon zest strips.
Increase heat to high and return stock to boil, then reduce heat to low.
Place about 2 cups of the soup into a blender and blend until smooth.
In a separate bowl: whisk eggs, yolks and lemon juice lightly until combined.While whisking constantly, slowly ladle about 2 cups of hot stock or broth into egg mixture; whisk until combined. Pour egg-stock mixture back into pot; cook over low heat, stirring constantly, until soup is slightly thickened, about 4 to 5 minutes. be sure to remove the soup from heat immediately or the eggs might begin to cook and the soup separates.
Add chicken. Taste and season with extra salt, pepper and lemon juice if necessary.
