Place drumsticks in a large bowl and carefully pierce the chicken pieces 3-4 times per sharp knife. This will help infuse the meat with the seasonings. Toss chicken with oil, soy sauce, lemon juice, garlic powder and salt. Marinate in the refrigerator for at least 30 minutes.
Pre-heat grill to high heat. Sear chicken in direct heat to form crust, about 2-3 minutes per side. Create an indirect heat source by turning off heat on one half of the grill (leaving the other half on high.) Move chicken to the side of the grill turned off to cook with indirect heat.
Grill chicken until internal temperature reaches 165°F rotating and basting every 2 minutes with BBQ sauce. Serve warm.