Turn your oven to 180 C / gas 4. Grease the baking tin(s).
Grate the rind off one of the lemons and then juice it.
Sift the flour and baking powder into a large bowl then and the 3 of the eggs, 175g of the sugar and the margarine. Beat everything together and then mix in the lemon rind and juice.
Divide the mixtures into the two tins and bake for 20-25 minutes.
While baking you can make the filling by whisking 2 eggs and then adding the remaining caster sugar. Add the rind and juice of the second lemon, and continue whisking. Cut up the butter and add it to the mixture.
Suspend the bowl over a pan of boiling water. Stir it from time to time as it thickens. It will take 20 minutes.
Once the cake and filling are both cooled to room temperature, spread the filling on one slice, then place the other one on top.
Finally, to make the icing mix the icing sugar and the juice of half a lemon. Drizzle over the icing and enjoy.