Preheat oven to 425 degrees.
Prepare artichokes by rinsing, then trimming 1 inch off tops and 1/2 inch off stems. Rub cut sides with one half of Meyer lemon. Slightly spread open petals around outside. Using your fingers, carefully open center to make room for garlic.
Cut another Meyer lemon half into 2 pieces. Stuff 1 lemon piece, 3 cloves garlic and sprig of thyme into center of each artichoke. Squeeze half a lemon over each artichoke, making sure to get juice into open petals. Drizzle 1 tablespoon olive oil over each. Liberally season with salt and pepper to taste.
Wrap each artichoke in double layer of heavy duty aluminum foil and place on baking tray. Roast for 1 hour to 1 hour and 15 minutes. Take tray out of oven and let cool for 15 minutes, being careful of steam. Open foil, and serve artichokes whole after drizzling with juices left in foil.