Pat the drumsticks dry with paper towels. This helps the skin crisp up and the seasoning stick better.
In a large bowl, whisk together olive oil, Cajun seasoning, smoked paprika, garlic powder, onion powder, cayenne, salt, black pepper, and lemon juice.
Add the drumsticks and toss to coat evenly. Let them marinate for 15 minutes if you have time, or proceed to cooking right away.
Preheat your grill to medium-high or oven to 425°F (220°C). If grilling, oil the grates lightly to prevent sticking; if baking, line a sheet with parchment for easy cleanup.
Arrange the drumsticks on the grill or baking sheet, leaving a little space between each piece for even cooking.
Grill: cook for 25–30 minutes, turning once or twice, until the skin is crispy and the internal temperature reaches 165°F (74°C). Oven: bake for 35–40 minutes, flipping halfway through, until the edges are caramelized and juices run clear.
If you like extra color and a slight glaze, brush on a thin coat of remaining marinade during the last 5 minutes of cooking.
Remove from heat and let rest for 5 minutes before serving to redistribute juices.