Preheat your oven to 350 degrees. Spray miniature muffin tins with vegetable oil cooking spray.
Mix cake mix, pudding mix, eggs and oil and blend well with an electric mixer until smooth, about 2 minutes. Pour a small amount of batter, filling each muffin tin half way.
Bake for 12 minutes. Turn out onto a towel.
To make the glaze, sift the sugar into a mixing bowl. Add the lemon juice, zest, oil, and 3 tablespoons water. Mix with a spoon until smooth.
Spoon the glaze over the warm cupcakes, turning them to completely coat. Place on wire racks with waxed paper underneath to catch any drips. Let the glaze set thoroughly, about one hour, before storing in containers with tight-fitting lids.