Squeeze the juice of three of the lemon halves into a bowl and fill the bowl with water.
Trim off a few of the dark outer leaves from the artichokes, then trim the stems up but leave them intact. Cut about a half-inch off the top of the artichokes. Thinly slice the artichokes about 1/8-inch thick, soaking them in lemon water as you work to prevent them from turning brown.
Heat the EVOO in large skillet with a tight-fitting lid over medium to medium-high heat. Add the onion and garlic and sauté for 5 minutes. Drain and dry the artichokes and add them to skillet, along with the bay leaves. Raise the heat for a bit, then season with salt and pepper. Lightly brown the artichokes, then stir in the wine and olives and cover the skillet. Reduce the heat to simmer and cook for 10 minutes more, until tender.
Uncover and reduce the liquid a final minute or two, douse with the juice of the remaining lemon half and transfer to a serving platter. Garnish with basil.