Preheat the oven to 325ºF (163ºC). Line the bottom of an 8 X 4-inch loaf pan with parchment paper. Grease and flour the insides.
In a medium-sized bowl, whisk together the flour, baking powder, salt and baking soda until well combined.
In a small bowl, whisk together the milk and sour cream until well blended.
In a large bowl, beat the sugar, oil, eggs, lemon zest, and strawberry extract, with an electric mixer on medium speed, until smooth, creamy and well blended. Mix in the food coloring, a little at a time, until your desired shade of pink is achieved.
Stir in the flour mixture in two additions, alternating with the milk mixture. Stir just until combined.
Transfer the batter to the prepared baking pan. Bake until a toothpick inserted into center of the loaf comes out clean, about 45-50 minutes. Meanwhile, prepare the lemon syrup.
Let the cake cool in the pan for 10 minutes, then remove from it from the pan and transfer it to a cooling rack. Poke holes all over the top of cake with a skewer. Brush the warm cake generously with the lemon syrup. Let the cake cool completely, then top with icing.