Heat the oven to 340 degrees. Spray two 9" round cake pans with coconut oil or similar oil, and set aside.
Combine the milk and lemon juice and set aside.
Combine the flour, baking powder, baking soda, and salt in a large mixing bowl.
In a separate bowl, combine the sugar, oil, milk, lemon juice, and lemon zest.
Slowly pour the sugar mixture into the flour, stirring until all clumps are removed.
Pour the batter into your two cake pans, and bake at 350 for 25-30 minutes, until a toothpick comes out clean. Cool completely.
For the icing
In a medium mixing bowl, combine the butter with the powdered sugar, 1/2 cup at a time, blending on medium speed. Add in the strawberries and milk, and blend until creamy. Add a tiny bit more milk if you like your icing creamier (no more than 1/2 tsp. at a time).
Put it all together
Remember, wait until the cakes are totally cool. I know. I hate this part. Then take a knife along the edge of the pan, and flip the cake over onto a plate or serving platter. Ice the top of the cake, and then remove the next cake, placing it on top. Ice the top, and then the sides. You'll probably have a bit of icing left over that you can eat by the spoonful (no judging) or use as extra for dipping (no judging).
Serve immediately. Cake will store in the fridge for a few days - just let it come back to room temperature before eating the rest of it. It tastes way better at room temp than it does cold, in my opinion, even though I can rarely wait long enough for it to warm up before eating.
Notes
Note: I've made this cake twice, and for my oven, the temp needs to be set at 340 degrees, otherwise the edges harden too much. You might need to bake this a tad longer if you set yours to 340, but it's worth it to not have crispy edges!