For the cake: Preheat the oven to 350 degrees F.
In a food processor, mix the sugar with the eggs, oil, yogurt, food coloring, vinegar, and vanilla. Add flour, cocoa, baking soda, and salt. Blend until just incorporated.
Place paper cupcake liners into a muffin pan, and divide the batter evenly among the cupcake liners, pouring only halfway so the batter doesn't overflow. Bake, rotating halfway through, for 25 to 30 minutes. Remove the cupcakes and let cool.
For the icing: In a bowl, beat the mascarpone, icing sugar, cream, and lemon zest together until the mixture is smooth.
Spoon a dollop of mascarpone cream on the cupcakes.