For the chicken and rub:
1. Combine lemon zest, salt and pepper in bowl. Rub zest mixture under chicken skin and tuck wings. Transfer chickens to rack set over rimmed baking sheet and refrigerate, uncovered, for 30 minutes. Note: chickens may be prepared up to this point 24 hours in advance. Allow chickens to sit at room temperature 30 minutes before grilling.
2. Open bottom grill vents completely. Light large chimney starter filled with charcoal briquettes (about 100) and burn until charcoal is covered with fine gray ash. Place 13 inch by 9 inch disposable aluminum roasting pan on one side of grill and pour hot coals into pile on opposite side. Evenly scatter 20 unlit coals and open fully. Let grill heat up 5 minutes. Scrape grate clean.
3. Dip wad of paper towels in oil and oil grate, holding paper towels with long-handled tongs. Place lemon halves cut side down over hot side of grill. Place chickens skin side down over cooler side of grill, with legs positioned closest to the coals. Cover, with opened vents in lid over chicken.
4. Grill lemons until deep brown and caramelized, 5 to 8 minutes. Transfer to bowl. Grill chickens until skin is well browned and breast meat registers 160 F, 45 to 55 minutes. Move chickens to hot side of grill and sear, uncovered, until deep brown, 2 to 4 minutes longer.
For the vinaigrette:
5. While chickens are grilling, squeeze 1/3 cup juice from grilled lemons into bowl. Using flat side of knife, mash garlic and salt into paste and add to bowl with lemon juice. Stir in mustard, sugar, pepper and parsley, then slowly whisk in olive oil until emulsified.
6. Transfer chickens to cutting board and let rest 10 to 15 minutes. Carve, transfer to serving platter, and pour 1/3 cup vinaigrette over chicken. Serve, passing remaining vinaigrette at table.
To prepare recipe on a gas grill:
Prepare recipe through step 1. Heat all burners on high, covered, for 15 minutes. Scrape cooking grate clean and oil cooking grate. Leave primary burner on high and turn all other burners to low. Place lemons over primary burner; place chickens, skin side down, over cooler part of grill, with legs positioned closest to heat; cover. Proceed with recipe from step 4, adjusting primary burner as necessary to maintain temperature 350 to 375 degrees. When chickens are cooked, transfer to hot part of grill and sear, uncovered, until deep brown, 2 to 4 minutes. Proceed with recipe from step 5.