Preheat oven or grill to 400 degrees.
Mix chopped garlic, cumin, oil, paprika, pepper, oregano, 1/2 tsp salt.
Peel the zest from one of the lemons. Add to garlic mixture.
Slice zested lemon into four equal pieces. Squeeze juice from two of the quarters and remaining whole lemon. Add 2 tbsp. juice into garlic mixture. Stir to combine.
Place the chicken breast side down on counter or work surface with legs pointing towards you. Cut along both sides of the backbone and remove it. Save for stock if desired. Open chicken like a book and turn breast-side up. Dry chicken with paper towels.
Using the remaining two lemon quarters, rub chicken all over. Squeeze the juice onto the chicken, then rub it with the lemon rinds.
At this point, you can loosen the skin to insert part of the spice mixture underneath. Do this carefully so the skin does not tear. Or just spread part of the mixture all over the bird. Top with remaining 1 tsp. salt.
Put chicken into a roasting pan, skin-side up. Roast chicken for 20 minutes, then baste it with the pan juices and some of the spice mixture. Continue to baste every 20 minutes, until a thermometer inserted into the thigh meat registers 165 degrees. This should take 50-60 minutes.
When chicken is fully cooked, remove it to a cutting board and let it rest 15 minutes before carving.
Place all ingredients into a blender or food processor and blend until well-combined. Transfer to a bowl and chill, covered, until your serving time.