Heat grill to medium heat.

In a large shallow bowl, combine 1 tablespoon of olive oil, 1/4 teaspoon of salt, and 1/4 teaspoon of lemon-pepper seasoning.

Add quartered red potatoes to the bowl and toss to coat evenly.

Place the coated potatoes into a grill basket.

Grill the potatoes over medium heat for 15 minutes, shaking the grill basket occasionally to ensure even cooking.

While the potatoes are grilling, place the trimmed asparagus spears in the same shallow bowl.

Add the remaining 1 tablespoon of olive oil, 1/4 teaspoon of salt, and 1/4 teaspoon of lemon-pepper seasoning to the asparagus; toss to coat.

After the potatoes have grilled for 15 minutes, add the asparagus to the grill basket with the potatoes.

Continue to cook for approximately 10 minutes, or until the potatoes are tender and the asparagus is slightly charred and tender, shaking the basket occasionally for even cooking.

Remove from grill and serve immediately.