Spoon lemon juice into milk and set aside for 10 minutes, until milk is "curdled" (this is a tip for turning milk into buttermilk. If you have buttermilk on hand, you can use that instead of the milk/lemon juice).
In a blender, puree the strawberries until smooth. Pour into a saucepan and simmer over medium heat until thickens slightly for about 5 minutes. Stir continuously. Once thickened slightly, allow to cool.
In a small bowl, whisk together the flour, baking powder, baking soda and 1/4 teaspoon salt. In a separate small bowl, stir together the milk/lemon juice mixture with only 1/3 cup of the strawberry syrup. Set remaining syrup aside for the glaze.
In the bowl of an electric mixer, beat together the softened butter and sugar on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl. Add the egg and vanilla and beat on medium speed until combined. Next, add the flour mixture alternating with the buttermilk mixture then flour mixture then buttermilk mixture. Beat each addition just until blended.
Either fill a pastry bag with the donut batter to pipe or use a small spoon to spoon the doughnut batter into prepared donut pan. (I found piping, although prettier, took longer and was more work. Using a small spoon worked just as well).
Bake for 10 minutes or until a toothpick inserted into the center comes out clean. Let cool in the pan for 5 minutes then remove to a cooling rack. Repeat filling/baking until all batter is used.