Preheat the oven to 350°F.
Spray miniature muffin tins with vegetable oil cooking spray. Combine the cake mix, pudding mix, eggs and oil and blend well with an electric mixer until smooth, about 2 minutes. (The batter will be thick). Pour a small amount of batter, filling each muffin tin half way. (I found a small cookie scoop the perfect thing for making them a uniform size).
Bake for 12 minutes. (I baked 4 dozen at one time, so it took a little longer--be sure to reverse places in oven for even baking if you cook this many. Also, they come out of the tin better if you cook a little past the golden brown stage so the cake is more firm). Turn out onto a tea towel.
Make the glaze while the cakes are baking. Sift the sugar into a mixing bowl. Add the lemon juice, zest, oil, and 3 tablespoons water. Mix with a spoon until smooth.
With fingers, dip the cupcakes into the glaze while they're still warm, covering as much of the cake as possible, or 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 1 hour, before storing in containers with tight-fitting lids.