Make the aioli by combining mayonnaise, garlic, lemon juice, fresh herbs, paprika, salt and pepper in a small bowl. Cover and refrigerate.
Cut each lobster tail in half lengthwise, pat pieces dry with paper towel. Brush lobster with olive oil and season with salt and pepper; grill, cut-side down, on medium-high grill for 2 min. Turn cut-side up and grill 2 min. more, or until just cooked through; serve immediately with garlic aioli.