Prepare a charcoal or gas grill for medium-high heat.
Melt the butter in a pan, then stir in the lemon juice and Worcestershire. Pour over the drumsticks in a large bowl and toss to coat. Sprinkle over the seasoned salt, lemon pepper and cayenne and toss again.
Grill the drumsticks in batches, turning occasionally, until cooked through, about 30 minutes.