In a small pan set over medium heat, add the chopped strawberries, lemon juice, and castor sugar. Heat until the sugar has melted and the strawberries soften.
Use a potato masher to macerate the softened strawberries. Once softened, allow the sauce to reduce until slightly thickened.
Once thickened, place the strawberry mixture into a food processor and blend it until smooth. Allow the strawberry sauce to cool before adding it to the frosting.
Strawberry Frosting
Add the butter and icing sugar to the bowl of a stand mixer fitted with a paddle attachment. Beat at medium speed until the mixture looks like fine breadcrumbs.
In a jug combine the milk and vanilla, with the motor of the mixer running at low speed slowly add the milk mixture. Continue until it has all been added. Then increase the speed of the mixer to medium-high. Beat until light and fluffy, scraping down the sides of the bowl often.
Add ⅓ cup of smooth strawberry sauce to the buttercream and beat at high speed until just combined. Place the buttercream into a prepared piping bag and use it to decorate cakes or cupcakes.