Arrange rack in middle of oven; preheat to 400°F.
IF GRILLING: Preheat gas grill to medium high heat. You'll want to start the chicken skin side down for a few minutes, until you get the gorgeous char marks. Then flip and finish cooking on low heat.
FOR CHARCOAL GRILLING: Start the chicken, skin side down, over direct heat. Once you get the char marks, move the chicken and finish cooking over indirect heat.
In a small bowl, mix garlic, cumin, oil, paprika, pepper, oregano, 1/2 tsp. salt, and finely grated zest from 1 lemon in a medium bowl.
Squeeze 1/2 of one of the lemons and add the juice to the rub, it should be 2 tablespoons. If you're short, squeeze the other half to get 2 tablespoons.
Quarter the remaining lemon, set aside the quarters.
Place chicken breast side down on work surface. Spatchcock chicken by cutting along both sides of backbone with kitchen shears. Remove backbone; reserve for stock. Turn chicken breast side up and splay open. Press down on breastbone with palms until you hear it crack and get the chicken as flat as possible.
Pat chicken dry with paper towels. Rub chicken all over with 2 reserved lemon quarters. Squeeze juice over bird.
Transfer chicken to rimmed baking sheet.
From both edges of cavity, gently loosen skin from breasts and thighs. Be careful not to tear skin. With your fingers, gently spread 2 heaping Tbsp. spice mixture under skin (reserve remaining spice mixture), then season chicken all over with remaining 1 tsp. salt.
FOR MAGICAL FLAVOR: Place the chicken in a bowl, cover and refrigerate for at least 6 hours. But if you REALLY want ALL the flavor, let it marinate all night.
Roast chicken 20 minutes, then brush with spice mixture and pan juices. Continue roasting, basting with spice mixture and pan juices every 20 minutes, until juices run clear when thigh is pierced with a fork or an instant-read thermometer inserted into thickest part of thigh registers 165ºF, 50-60 minutes total.
Transfer chicken to a cutting board and let rest 15 minutes, reserving pan juices.