Preheat your smoker to 250°F.
Pat the chicken dry with paper towels. Place the chicken breast-side down on a cutting board. Using kitchen shears, cut along both sides of the backbone to remove it. Flip the chicken over and press down firmly on the breastbone to flatten it.
Drizzle olive oil over the chicken and rub it in evenly.
In a small bowl, mix together smoked paprika, garlic powder, onion powder, thyme, salt, black pepper, and cayenne pepper (if using). Rub the spice mixture all over the chicken, ensuring it gets into all the nooks and crannies.
Place the halved lemon inside the cavity of the chicken.
Transfer the chicken to the smoker, breast-side up. Smoke for about 1.5 to 2 hours, or until the internal temperature reaches 165°F in the thickest part of the breast.
Once cooked, remove the chicken from the smoker and let it rest for 10-15 minutes before carving.