Have guests unwrap these packets at the table; the paper will give waytoafragrant mix of baby artichokes,olives, and thyme sprigs.
Preheat oven to 350 degrees. Cut four 16-by-13-inch pieces of parchment paper; set aside. Fill a medium bowl with water; squeeze 1/2 lemon into water. Cut each artichoke in half lengthwise. Remove tough outer leaves; trim sharp tips with scissors and stems with a paring knife. Transfer to lemon water to prevent discoloration.
Place about 12 thyme sprigs and a few garlic slices in center of 1 piece of parchment; top with 4 artichoke halves. Season with salt and pepper. Drizzle with 2 teaspoons lemon juice, then 1 tablespoon oil. Place 4 olives on top.
Make a parchment packet: Bring long sides of parchment together. Make 1/2 inch fold, and crease; repeat twice, creasing firmly after each fold. Fold short ends downward, 2 or 3 times, creasing firmly after each fold. Tuck folded ends under packet; transfer to a baking sheet.
Repeat with remaining thyme, garlic, artichokes, lemon juice, and oil, for a total of 4 packets. Bake until artichokes are tender when pressed through packet, 25 to 30 minutes. Serve packets on plates with aioli and lemon wedges.
If baby artichokes are unavailable, you can use 2 medium artichokes. Prepare as directed; remove the fuzzy chokes. Cut halves into 3 wedges, and divide among the 4 packets.