Preheat oven to 300°. Squeeze enough lemons to make 1/4 cup juice. Slice remaining lemons very evenly 1/8 to 1/4 in. thick, using a thin serrated knife. Discard seeds and end pieces. Layer slices in an 8- or 9-in. square glass baking dish.
Meanwhile, bring 1 1/2 cups water, the sugar, and corn syrup to a boil in a small covered saucepan. Reduce heat to medium and boil 1 minute. Remove from heat and stir in lemon juice. Pour over fruit and cover dish tightly with foil.
Bake until fruit is tender and somewhat translucent but still keeps its shape, 50 to 55 minutes. Uncover and bake until syrup reduces by a third, about 30 minutes. Let cool to room temperature, then use or chill, covered. Lift out slices with a fork and drain to use.