Preheat oven at 350F.
Combine sifted flour, baking powder, salt, and half amount of sugar in a mixing bowl fitted with whisk attachment on a stand mixer.
Combine egg yolks, oil and water. Add the yolk mixture gradually to the dry ingredients on medium mixing speed. After a paste has formed, use a spatula to scrape down the sides of the bowl.
Continue adding the yolk mixture until everything is incorporated. Set aside (or transfer to another bowl if you only have one mixing bowl for your mixer, remember to wash mixing bowl and whip attachment before using for egg whites).
Combine egg whites and lime juice and whip on medium speed with a clean whisk until frothy. Gradually add the remaining sugar while continuing to whip. Stop when medium peaks has formed.
Fold one-third of the beaten egg whites into the yolk mixture to lighten it. Gently fold in the remaining beaten egg whites. The more quickly the two egg mixtures are incorporated, the less the amount of volume lost.
Quickly pour the batter in a lined half sheet pan. Use an offset spatula to even out the surface. Then put it in the oven and bake until the cake springs back when touched, 20 to 30 minutes.
When the cake is done cooking. Take it out of the oven. Wait for 2 minutes then carefully transfer it (with parchment paper) to another half sheet pan or big cutting board.
Wait for another 3 minutes, then carefully roll the cake into a log using parchment paper. Do not remove parchment paper. At this step, the cake is supposed to rolled with parchment paper inside it to help keep a rolling shape.
Let the rolled cake cool completely to room temperature.