Preheat the oven to 180C/350F. Line an 8-inch pan with parchment paper and set aside.
In a large mixing bowl, add your flour, sugar, baking soda, and salt and mix well. Once mixed, add your vinegar, oil, water, lemon juice, lemon extract and mix well.
Transfer your lemon cake batter to the square pan. Bake for 25-30 minutes, or until a toothpick comes out just clean.
Remove from the oven and let cool in the pan completely. Once cool, frost if desired.
To make the frosting, beat together the vegan cream cheese, butter, vanilla extract, and lemon juice until smooth. Slowly add in the confectioners sugar until fluffy.
Notes
* Any sugar works. If you use coconut sugar or brown sugar, your cake will be darker.** For a more pronounced lemon flavor, replace more of the water with lemon.TO STORE: Leftover cake will keep well at room temperature, covered, for up to three days. If you want to keep it longer, store the cake in the refrigerator. TO FREEZE: Place slices of the cake in an airtight container and store them in the freezer for up to 6 months.