Whatever you think of modern-day Rose's Lime Cordial (other brands are available as well as homemade recipes), as with the Gimlet, I believe lime cordial...
We don't use lime cordial at all, since all of the commercial ones we've ever tried are, to our taste, terrible. We weren't aware of the Morgenthaler recipe and, since we make our own passionfruit and lemon syrups, will give it a go. Thanks a lot for the tip.