I'd say at a fairly rudimentary guess, they took cream of chicken soup, added a little rice and lemon flavoring. Penzey's carries a powdered lemon flavor which I am adding to my list to pick up next time I go to Santa Rosa. There was not much rice or chicken in it, which I would change. I can't imagine it would be that simple.

Avgolemono Sauce

1 cup chicken stock
2 tbsp butter
2 tbsp flour
4 tbsp lemon juice (approx. one large lemon)
2 eggs
2 tbsp water
1/8 tsp cayenne
1/2 tsp black pepper
salt to taste, unless using soup base that contains salt

Heat the stock.

Make a roux with the butter and flour and add the stock. In a separate bowl, lightly beat the eggs and add the lemon juice and water. Slowly add this mixture to the thickened stock, stirring constantly, and heat to desired temperature. Add pepper and salt, as needed.

For soup, add more stock and pieces of chicken. I usually add cooked noodle (especially wide egg noodles), you can use cooked rice instead.