Preheat the oven to 180°C (350°F) and prepare a rectangular cake tin with oil or cooking spray and parchment paper.
Add the oil, eggs, and sugar to a bowl of a stand mixer fitted with a whisk attachment. Beat on medium-high speed until combined, about 2 minutes.
Sift together the salt, baking powder, and flour then add the flour mixture to the egg and sugar mixture. Beat at low speed until just combined.
In a jug combine the milk and vanilla, and slowly pour this into the cake batter with the mixer's motor running at low speed. Scrape down the sides of the bowl and mix again, making sure it is lump-free.
Pour the cake batter into the prepared cake tin and bake it in a preheated oven for 25 to 30 minutes or until a skewer inserted into the centre of the cake comes out clean. Allow the cake to cool in it tin for 30 minutes then transfer it to a wire rack to cool completely.
Raspberry Purée
Add the raspberries, lemon juice, and castor sugar to in a small saucepan set over medium heat. Allow the fruit to soften and the sugar to melt, stirring occasionally.
With a rubber spatula press the fruit against the sides of the saucepan to help larger pieces of raspberries break down. Once the purée has thickened, remove the puree from the heat and transfer it to a glass jar to cool to room temperature.
Raspberry Buttercream
In a bowl of an electric mixer fitted with a paddle attachment, add the butter and icing sugar. Beat at medium speed until the mixture looks like fine breadcrumbs.
In a jug combine the milk and vanilla, with the mixer's motor 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 the cooled raspberry puree to the whipped buttercream, and beat again until combined.
Place the cooled cake onto a large plate and spread the remaining pureed raspberries over the top of the cake. Spoon the frosting onto the puree and spread it out with a pallet knife over the entire cake, swirling the puree into the frosting. Slice and enjoy!