For the Lemon Swiss Roll Cake
Preheat the oven to 350 F (176 C) and prepare a 10 x 15 inch cookie sheet by lining it with foill. Grease the foil with oil, and flour it well. This will help to ensure that the cake does not stick to the foil.
In a medium bowl (or the bowl of a stand mixer) beat the eggs on high speed for about 2-3 minutes, until pale and frothy.
Add in the sugar, lemon juice and lemon zest. Beat on high speed until well combined.
In a separate bowl, whisk together the salt, baking powder and flour. Add the dry ingredients to the wet ingredients, and stir until just combined. Do not over mix.
Pour the cake batter onto the prepared cookie sheet. You may have to use a spatula to spread out the batter over the cookie sheet and the batter will be spread out in a very thin layer.
Bake for about 10-11 minutes.
While the cake is baking, spread out a clean kitchen towel and sprinkle liberally with icing sugar (this is to ensure that when the cake is placed onto the kitchen towel, it will not stick).
As soon as the cake is done, take it out of the oven, and carefully turn it over onto the prepared kitchen towel. Gently peel off the foil, and working quickly start rolling the kitchen towel to roll the cake from the shorter edge. Let cool completely.
For the Lemon Cream Cheese Filling
In a medium bowl, using a hand mixer or a stand mixer, beat the cream cheese and butter on medium speed until smooth and well combined. This will take about 1-2 minutes, and you should scrape down the sides of the bowl with a spatula as needed.
Add the sugar, lemon juice, lemon zest and vanilla, and beat on medium speed for about 2 minutes until well combined and thick.
Assembling the Lemon Swiss Roll
Once the cake has completely cooled down, unroll it from the kitchen towel. Spread the cream cheese filing liberally, making sure that it covers all ends. Gently roll back the cake into shape, and cover with cling film. Cool for about 2 hours in the refrigerator or overnight.
When ready to serve, unwrap the cling film, dust the cake with icing sugar and decorate with lemon slices.