Preheat the oven to 350 degrees F. Make the cake: Brush a rimmed 11-by-17-inch baking sheet with vegetable oil and line with parchment paper. Oil the parchment and dust with potato starch, tapping out any excess.
Spread the coconut on a separate baking sheet; bake until lightly toasted, about 8 minutes. Let cool. Finely grind all but 1/4 cup coconut in a food processor; add the matzo meal and process until finely ground. Transfer to a large bowl and stir in the potato starch and salt.
Combine 1/4 cup vegetable oil with the lemon zest and juice in a bowl; set aside. Put the eggs in their shells in a bowl and cover with hot tap water; let stand 5 minutes. Crack the eggs into a bowl; add the granulated sugar and beat with a mixer on medium-low speed until combined, 1 minute. Increase the speed to medium high and beat until thick and fluffy, 12 minutes. Fold the egg mixture into the matzo meal mixture with a rubber spatula until combined. Stir in the lemon-oil mixture until just combined. Spread the batter on the baking sheet; bake until the cake is golden and springs back when pressed, 18 to 20 minutes. Transfer to a rack and let cool 5 minutes in the pan; run a knife around the edge of the cake to loosen.
Dust a kitchen towel with confectioners' sugar and invert the cake onto the towel. Peel off the parchment. Starting with a long side, carefully roll up the cake, using the towel to help you. Wrap the towel tightly around the rolled cake and let cool completely, about 15 minutes.
Make the frosting: Put the egg whites, granulated sugar, lemon zest and juice, and salt in a heatproof bowl. Set the bowl over a saucepan of simmering water (do not let the bowl touch the water); whisk until the sugar is dissolved, 3 minutes. Remove the bowl from the pan and beat with a mixer on medium-high speed until thick, glossy and cool, 3 to 5 minutes.
Assemble the cake: Unroll the cooled cake and spread with the raspberry jam. Reroll the cake, cover with the frosting and top with the reserved 1/4 cup coconut. Serve with raspberries.