Preheat oven to 350° F and line a regular muffin tin with paper liners. 

In a large bowl, whisk together the milk, vegetable oil, eggs, and vanilla. Add the sugar and whisk to combine. 

Next, add the flour, baking powder, and salt. Mix just until no large lumps of flour remain. 

Gently fold in the diced strawberries.

Divide the batter evenly between the 12 muffin wells.

Bake for 18-20 minutes, or until a toothpick inserted into the center comes out just clean. 

Remove the cupcakes to a wire rack and let cool for 10 minutes. Then remove cupcakes from the pan and let cool completely before frosting. 

Place strawberries and lemon juice in a food processor and pulse until they form a smooth puree, about 1 minute. 

Strain the strawberry sauce through a fine mesh sieve, extracting as much liquid as possible. If your sieve is not very fine, add a layer of cheese cloth before pouring in the strawberry sauce. Discard the seeds. 

Add the softened butter to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed until the butter is very smooth, about 30 seconds. 

With the mixer on low speed, slowly mix in the powdered sugar. 

Once all of the powdered sugar has been incorporated, add the smooth strawberry puree and vanilla extract. 

Turn the mixer to high speed and beat for 1-2 minutes, or until the frosting is very light and fluffy, scraping down the bowl as needed to keep everything incorporated. If you'd like the frosting sweeter or thicker, add more powdered sugar, a bit at a time, whipping after each addition.

Transfer the buttercream to a piping bag and frost the cooled cupcakes as desired - or simply add the frosting using an offset spatula or even a spoon.