Grilled Lemon Shandy

Light a grill and set it up for direct heat or preheat a grill pan. Oil the grates and grill the halved lemons cut side down over high heat until nicely browned, 4 to 5 minutes. Meanwhile, grill the lemon slices, turning once, until nicely charred on both sides, 4 to 5 minutes. Transfer to a plate and let cool slightly. Squeeze the juice from the halved lemons into a liquid measuring cup until you have about 3/4 cup. In a pitcher, combine the grilled lemon juice with the simple syrup and the ice water. Stir until the lemonade is well chilled. Pour the beers into six large glasses and top each with about 1/2 cup of lemonade. Garnish with a grilled lemon slice and serve.