Remove giblets, if any, and rinse the chickens, inside and out, under cold running water. Dry thoroughly with paper towels. Tie the legs together with butcher's string and tuck the wings behind the backs.
Make the spice paste: In a small bowl, combine the garlic, salt, and pimenton and blend well. Stir in 3 tablespoons of olive oil. Smear the mixture all over the outside of the chickens. Tuck one bunch of thyme inside the main cavity of each bird. Place on a rimmed baking sheet and refrigerate, uncovered, for at least 6 hours or overnight.
Place the potatoes in a large bowl and season with salt and pepper. Drizzle with the remaining 3 tablespoons of oil and toss to coat. Spread the potatoes in a large roasting pan or on a large rimmed baking sheet.
Arrange the chickens side by side on top of the potatoes. Squeeze the lemons over the chickens and add the rinds to the potatoes.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 400-450F and preheat, lid closed, for 10 to 15 minutes.
Roast the chickens, potatoes, and lemons for 30 minutes. Stir the potatoes. Reduce the temperature to 350F and continue to roast until an instant-read meat thermometer inserted into the thickest part of the thighs registers 165F, about 40 minutes more.
Transfer the chickens to a cutting board; let rest for 10 minutes.
Arrange the potatoes and lemons on a large platter. Dust lightly with pimenton and garnish with the parsley. Arrange the chickens on top. Enjoy!