Cut 2 lemons in half; squeeze juice into water, and drop lemons in water. Peel tough outside leaves from artichokes. Cut off stem ends; trim about 1/2 inch from each top. Cut trimmed artichokes in half lengthwise; immediately place in prepared water.
Heat olive oil in a large nonreactive pot over medium-low heat. Stir in fennel and next 5 ingredients. Slice remaining lemon, remove seeds, and place in fennel mixture. Stir in salt and pepper. Cover and cook 15 minutes.
Drain artichokes, and add to fennel mixture. Cover and cook, stirring frequently, for 30 minutes or until artichokes are tender. Remove bay leaf. Season to taste with salt and pepper. Serve with a slotted spoon.