Position an oven rack about 8 to 10 inches from the broiler and preheat. Grate the lemon zest and combine in a small bowl with the butter, garlic, 1/2 teaspoon salt, and pepper to taste. Mash with a fork to make a smooth paste.
With your fingers, gently loosen the skin on the chicken breasts, legs and thighs. Spread the flavored butter under the skin as evenly as possible. Halve the lemons and squeeze 2 halves over the chicken; season with salt and pepper.
Place the chicken skin-side up on a broiler pan (or a rack on a baking sheet). Position the halves about 2 inches apart with the thick parts of the legs facing the center. Arrange the remaining 2 lemon halves cut-side down next to the chicken.
Broil the chicken until the skin is light brown and crisp, about 8 minutes. If the chicken browns too quickly, lower the oven rack. Flip the chicken and the lemons and continue to broil until almost cooked through (a thermometer inserted into the thickest part will register 160 degrees), about 15 minutes. Remove the lemons, if browned; turn the chicken again and broil until the skin is brown and crisp and the thermometer registers 165 degrees, about 2 more minutes. Serve the chicken with the broiled lemons for squeezing on top.