To make the candied lemon, combine the sugar, water, and lemon slices in a wide saucepan and bring to a boil.
Reduce the heat to medium-low and simmer the lemon slices for 20 minutes or until the peels are translucent.
Transfer the slices to a rack to cool and allow to dry for at least 8 and up to 24 hours.
For the lemon curd, whisk together the yolks and sugar until pale yellow in a medium bowl.
In a medium saucepan, combine the lemon juice, butter, salt, and zest, heating gently until the butter has melted.
Temper the egg mixture by slowly drizzling in the warm butter mixture, whisking constantly.
Transfer the curd base back to the saucepan and cook over medium-low heat, stirring constantly with a wooden spoon until thickened but not boiling.
Strain the curd into a medium glass bowl.
Cover the curd with plastic on the surface to prevent a skin from forming and place the bowl in the refrigerator to chill completely while baking the cakes (about 1 hour).
Preheat the oven to 350 F.
Grease and line the bottoms of two 9-inch round cake pans with parchment paper.
Create a double boiler by bringing an inch of water to a simmer in a saucepan.
Turn off the heat and place the white chocolate in a heat-proof bowl over the pan, stirring frequently until the chocolate is melted. Remove the bowl and set aside.
In a separate bowl, whisk together the whites and vanilla extract until slightly foamy.
In a large mixing bowl, combine the flour, sugar, baking powder, and salt.
Add the butter and milk and use a hand mixer (or stand mixer) to incorporate on low speed, then increase the speed to high and beat for a minute longer.
Add the egg white mixture in two batches, beating for about 30 seconds after each addition and scraping down the sides of the bowl.
Add the melted and cooled white chocolate and beat until fully incorporated.
Divide the batter between the two cake pans and smooth the tops
Bake the cakes for 25-30 minutes or until they're light golden brown and a toothpick inserted in the center comes out clean.
Cool the cakes completely in the pans on racks, then turn them out.
While the cakes are baking prepare the lavender simple syrup by combining the sugar, water, and dried lavender in a small saucepan.
Bring the mixture to a boil, turn off the heat, and cover for 30 minutes to steep.
Strain the syrup into a jar or small bowl to cool and set aside.
Start the buttercream by adding the water and ¾ cup of the sugar to a small saucepan.
Stir until the sugar is dissolved. Slowly heat the mixture while constantly stirring until it starts to bubble.
Continue to cook until large bubbles form.
Meanwhile, in a stand mixer beat the egg whites and salt until foamy.
Add the cream of tartar and beat until soft peaks form.
Gradually add the remaining ¼ cup sugar and beat until stiff peaks form.
Slowly and carefully drizzle the cooked sugar mixture into the whipped egg whites with the mixer running constantly.
Beat at high speed until the mixture has cooled to room temperature (this may take up to 10 minutes).
Turn the mixer down to medium speed and add the vanilla and lavender extracts. Add the butter one piece at a time until the mixture comes together and is silky, increasing the speed once the butter is incorporated.
To assemble the cake, place one layer on a plate or platter.
Brush on some of the simple syrup to moisten the top.
Use a pastry bag fitted with a large round tip to pipe a circle of buttercream around the edge of the cake top. This helps hold in the filling.
Spread the lemon curd evenly on the cake.
Brush the top of the second cake layer with the syrup and place it top-side down on the lemon curd.
Brush the cake with the remaining syrup.
Ice the cake with the buttercream, adding decorative piping or food coloring, if desired. Press the candied lemon slices into the icing on the sides of the cake or use to garnish the top.
Chill the cake completely and then slice and serve. Cover and store the leftover cake in the refrigerator.