Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well combined.
In a large bowl, mix the unsweetened applesauce, granulated erythritol, and honey until smooth.
Add the eggs one at a time to the wet mixture, beating well after each addition.
Stir in the Greek yogurt, fresh lemon juice, lemon zest, and vanilla extract until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 38 to 42 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.