Put the sugar, 1/4 cup water and the corn syrup into a small saucepan and stir until the sugar is dissolved. Bring the mixture to a boil over medium heat and cook, without stirring, until the syrup registers 240 degrees F (soft-ball stage) on a candy thermometer, about 5 minutes.
Meanwhile, while the sugar is cooking, put the egg whites in the bowl of a stand mixer fitted with a whisk attachment and whip on medium-low speed until foamy, about 1 minute. Sprinkle in the cream of tartar and increase the mixer speed to medium; whisk until soft peaks form, about 3 minutes.
When the syrup reaches the correct temperature, reduce the mixer speed to low and slowly drizzle the hot syrup down the inside of the mixer bowl in a slow, steady stream (be sure not to let the syrup hit the whisk to avoid splattering). Increase the mixer speed to high and whip until the whites are stiff and glossy, about 4 minutes.
Use the meringue immediately to top a lemon meringue pie.