Place 3 lemon halves, squeezing their juice out first, into a large pot of lightly salted (2 tsp salt) water, and then bring to boil. Wash artichokes. Pull off lower, tougher outer petals (leaves), cut stems to inch or less. Snip off sharp tips of remaining petals. Place in the pot and adjust heat so they gently simmer. Cover and cook 20-30 minutes, or until a petal near the centre easily pulls out. Drain well and cool to room temperature. Gently spread out leaves and then pull out centre leaves to expose the hairy choke. Remove choke with a small spoon. Place artichokes on plates. Divide and spoon pesto mayonnaise into the centre of each artichoke and serve.
Note: Artichokes and mayonnaise can be prepared a day in advance and kept stored in the fridge.