Set steamer basket inside large pot; add water to just below basket. Squeeze juice from 1 lemon into water; drop lemon into basket. Add thyme sprigs. Bring water to a boil.
Using a serrated or chef’s knife, cut about an inch off top of each artichoke. Trim off part of stems so artichokes sit upright; peel stems if desired. With scissors, trim sharp tips from leaves. Remove any tough exterior bottom leaves. Rub cut surfaces of artichokes with half of remaining lemon. Use other half of lemon for aioli.
Place artichokes in steamer basket, bottom side up. Cover; steam for 30 to 45 minutes or until leaves pull away easily and heart or stem is tender when pierced with knife. Add more water while steaming, if needed. Do not let pot boil dry.
Combine mayonnaise, lemon juice, lemon peel, garlic and bouillon in small bowl; stir well. Season with pepper. Serve with cooled or chilled artichokes.
Lemon Aioli can be made in advance. Cover and refrigerate for up to 1 week.