Combine the lemon juice, oregano, coriander, garlic, and ½ cup olive oil in a small food processor and blend until chopped and combined (no need for total smoothness).
Set aside half the mixture and Marinate the chicken thighs in the remaining half for at least an hour but up to a day.
Remove the thighs from the pan, roughly chop into bite sized pieces, and put chicken pieces and any juices into the reserved marinade and refrigerate. Don't wash your pan.
Meanwhile, make the rice:
In a 2 quart pot, melt the butter over medium high heat, and add the spices and cook for about 30 seconds to a minute. (Smell that? That's one of the good New York smells. Now you can get it without the tinge of diesel fumes and garbage!).
Add the rice and stir until the rice is coated in the butter and lightly toasted, a couple of minutes.
Add the chicken broth, stir, cover, reduce heat and cook over low heat for 15 minutes, or until rice is tender.
Make the sauce:
Combine all the ingredients for the sauce, and adjust according to taste. (The Nuni loves tasting and saying, "I think just a little more lemon juice. Don't you, mom?")