Cook pasta according to package directions, omitting salt and fat. Drain pasta, reserving 1/2 cup cooking liquid. Set pasta aside; keep warm.
Combine 2 cups water and juice in a medium bowl. Working with 1 artichoke at a time, cut off stem to within 1/4-inch from the base; peel stem. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom; trim about 1 inch from top of artichoke. Cut each artichoke in half lengthwise. Place artichoke halves in lemon water.
Heat 1 tablespoon oil in a large skillet over medium heat. Drain artichokes well; pat dry. Add artichokes to pan. Cover and cook 8 minutes, stirring occasionally; uncover. Increase heat to medium-high; cook 2 minutes or until artichokes are golden, stirring frequently. Place artichokes in a large bowl.
Place pan over medium heat; add remaining 1/4 cup water and asparagus to pan. Cover and cook 5 minutes or until crisp-tender. Add asparagus, parsley, and rind to artichokes; toss well. Add pasta, reserved cooking liquid, the remaining 2 tablespoons oil, thyme, salt, and pepper to artichoke mixture; toss well. Place 2 cups pasta mixture into each of 6 shallow bowls; top each serving with about 3 tablespoons cheese.