Spray miniature muffins 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.
Pour a small amount of batter, filling each muffin tin half way. Bake for 12 minutes. Turn out onto a tea 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.
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.