Preheat the oven to 350°F. Pick the lilac blossoms from the stem and discard the leaves and stems which can impart a bitter flavour. Combine the sugar and lilac blossoms in a food processor. Pulse until the petals are mostly broken down but don't over blend. Set aside.
In a small mixing bowl combine the flour, baking powder, baking soda, and salt. Whisk together to combine. In a small measuring cup combine the milk and lemon juice. Whisk together and set aside.
In the bowl of a stand mixer combine the softened butter and lilac sugar. Beat using a paddle attachment until the butter and sugar are fully incorporated and creamy. Scrape down the sides as needed and beat until combined.
Add the eggs one at a time to the mixer, beating in between to ensure the egg is fully incorporated before adding the next egg. Scrape down the sides as needed.
Add one third of the flour mixture to the mixer and beat on low just until the flour is mostly incorporated. Add half of the soured milk and beat just until it is mostly incorporated. Repeat with another third of the flour and the rest of the milk. Add the last of the flour mixture and beat on low just until the batter is fully combined.
Spray a mini bundt cake mold generously with non-stick or bakers' spray. Drop the cake batter into the mini bundt cake pan, making sure to fill in all the crevasses. Spread the batter evenly and tap the cake pan a few times on the counter to remove any air pockets.
Bake the cakes for 20 to 25 minutes until a toothpick comes out clean and the top springs back once touched. Transfer to a rack.
While the cake is baking, make the lilac infused syrup. In a small saucepan, combine the sugar and water. Place over medium high heat and bring to a simmer, stirring until the sugar is completely dissolved.
Once the syrup comes to a simmer, remove from the heat and add the lilac blossoms. Cover and let steep until the cakes have finished baking. Strain and discard the blossoms. Set aside two tablespoons of the syrup to use in the glaze.
In a small bowl, whisk together the icing sugar, reserved lilac syrup, and milk. Whisk until smooth. Add a little violet food colouring. Add more milk or icing sugar as needed to create a pourable glaze that isn't too runny.
As soon as the cakes are finished baking, transfer the pan to a wire rack. Generously brush the tops (what will be the bottoms) of the cake with some syrup. Let cool for no more than 5 minutes. Turn the cakes out of the pan onto parchment paper.
Brush the tops of the mini cakes with more syrup and let cool. Once the cakes are cool, drizzle with the glaze and allow to set. Enjoy!