The bags of sugar which she bought contain 2 * 6 = <<2*6=12>>12 cups.
In total, she has 12 cups + 3 cups = <<12+3=15>>15 cups of sugar to use.
She needs 1 cup + 2 cups = <<1+2=3>>3 cups of sugar to make the batter and frosting for a dozen cupcakes.
Lillian has enough sugar to bake and ice 15 / 3 = <<15/3=5>>5 dozen cupcakes.
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