Funny you should mention that. I’ve done a lot of experimenting with sugar in cakes, superfine versus baker’s sugar versus granulated, and I always found I got a finer texture with superfine.
However I had a funny experience during an experiment I did with Italian meringue. Against the conventional wisdom I discovered that I could make it with tubinado sugar instead of regular granulated sugar. I would have thought some residual something, maybe the large crystal size or more likely the molasses in it would have prevented the meringue from whipping stiffly, but the turbinado sugar dissolved beautifully and the meringue was wonderful. All you have to do is let the turbinado sugar sit in the egg whites for five minutes, then you beat the whole thing together at once instead of adding the sugar gradually.
Having made that discovery I started trying experiments with cake, and I discovered I could get get just as fine a texture with it. For this recipe I thought that combined with the lemons it would be a nice flavor.