Combine the strawberries and lemon juice in a blender or a small food processor. Purée until smooth. You should end up with 1 cup. Transfer the puréed strawberries to a medium-sized saucepan. Bring to a boil over medium heat. Turn the heat down and simmer until the purée is reduced by half, about 10-12 minutes. Remove from heat and set aside to cool to room temperature. Set aside 2 tablespoons (30ml) of the cooled strawberry reduction for the icing.
Preheat the oven to 325ºF (165ºC). Line a 9-inch by 5-inch loaf pan** with parchment paper.
In a medium-sized bowl, whisk together the flour, baking powder, baking soda, and salt until well blended.
In a large bowl, beat the butter and sugar together, with an electric mixer on medium speed, until pale and fluffy. Add the oil and beat until the mixture is creamy and well blended. Beat in the eggs in 2 separate additions, until emulsified. Add the extracts, then mix in the food coloring (if using) a little at a time until your desired shade of pink is achieved. The color will fade a bit during the baking process.
On low speed, or by hand, stir in the flour mixture in 3 additions, followed by the strawberry reduction after the first addition, then alternating with half of the buttermilk after the last 2 additions. Mix just until combined. Transfer the batter to the prepared loaf pan. Bake until the top of the loaf is golden brown and a toothpick inserted into the center comes out clean, about 35-40 minutes. Cool the cake in the pan for 10 minutes, then remove it from the pan and transfer it to a cooling rack.