Preheat the grill to medium heat, about 375–400°F. Set it up with a cooler side and a hotter side if possible.
Pat the chicken wings very dry with paper towels. Add them to a large bowl with olive oil, black pepper, and Cajun seasoning. Toss until evenly coated.
Grill the wings over medium heat for 20–25 minutes, turning often, until the skin is golden, crisp, and the wings are cooked through. Move them to a cooler part of the grill if they start to darken too quickly.
While the wings grill, make the Cajun butter. In a small saucepan over medium-low heat, melt the Challenge Unsalted Butter. Stir in the Cajun seasoning and lemon juice until combined.
During the last few minutes of grilling, brush the wings with some of the Cajun butter and turn once or twice until glossy and lightly caramelized.
Transfer the wings to a large bowl and toss with more Cajun butter, or arrange them on a platter and drizzle the butter over the top.
Serve warm with lemon wedges, ranch, blue cheese dressing, or celery sticks, if desired.
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