Stir together first 6 ingredients, 5 tablespoons of the oil, 1 teaspoon of the salt, and 1⁄2 teaspoon of the black pepper in a medium bowl. Add chicken; toss to coat. Chill 1 hour.

Preheat grill to medium-high (400°F to 450°F). Toss asparagus and lemon slices with remaining 1 tablespoon oil. Remove chicken from marinade; discard marinade. Thread chicken, asparagus, and lemon slices tightly onto 8 (8-inch) skewers, folding chicken strips and lemon slices in half as needed. Sprinkle with remaining 1 teaspoon salt and 1⁄2 teaspoon black pepper. Place kebabs on lightly greased grill grate. Grill, uncovered, until asparagus is tender and chicken is charred and cooked through, 12 to 14 minutes, turning occasionally.