Preheat the oven to 350°F. Coat an 8" round or square baking pan with nonstick cooking spray, and line the bottom and sides with parchment paper.
Remove any visible seeds from the lemons. Blend sugar and Meyer lemons in a food processor for 1 minute until smooth.
Whisk the eggs vigorously by hand or with an electric mixer until thick and frothy, about 2 minutes. Add the oil and whisk for another minute or so.
Incorporate the labneh by whisking for about 30 seconds, then add the Meyer lemon mixture until light and fluffy and thoroughly combined.
Sift almond flour, baking powder, and kosher salt into the bowl with the wet ingredients. Stir the mixture until no dry spots are remaining. Transfer the combined mixture to the prepared pan.
Bake the cake for 40-45 minutes or until the edges turn golden brown and the center fully sets without jiggling. Allow the cake to cool completely, then, if desired, dust it with powdered sugar and top it with whipped cream before slicing and serving.
Store the cake tightly wrapped at room temperature for up to 1 day or refrigerate for up to 1 week.
