Preheat oven to 350° and line a round springform pan with parchment paper and grease the sides with coconut oil; set aside.
First, make the flax eggs by stirring the flaxseed meal and water together and letting the mixture sit for 5-10 minutes. Next, cream the butter and sugar together in a large mixing bowl. Then, add the flax eggs, yogurt, vanilla, and vinegar and stir to combine.
To that same bowl, add the flour, baking soda and lavender and stir until combined. The batter will be slightly sticky and on the thicker side -- that's ok! Transfer the batter to your prepared pan, using a rubber spatula or the back of a spoon to smooth it out.
Next, make the crumb topping: stir the flour, brown sugar, cinnamon, and lavender together in a small bowl, then add the butter and use your hands to combine everything until small crumbs form (this will probably take a minute or two).
Sprinkle the crumb topping over the cake batter. Place your springform pan on top of a baking sheet (to prevent any accidental spillage), then into the oven. Bake the cake for 45-55 minutes, or until a toothpick comes out clean.
Leave the cake in the pan for 30 minutes, then remove it from the springform pan and transfer it to a cooling rack. Allow the cake to cool before cutting it. Enjoy!