Pack artichokes upright in a large pot. Add garlic. Pour in water. Bring to a boil. Reduce heat. Simmer, covered, for 35 minutes. Transfer to a plate; let cool. Peel and mash 4 steamed garlic cloves (reserve remainder for lamb). Stir in mayonnaise, zest, lemon juice, pepper, sugar, and salt. Remove artichoke leaves (reserve hearts for stuffing). Refrigerate leaves and aioli separately until ready to serve.