The Lychee Lani recipe comes from the folks at Modern Tiki, a blog (and book!) devoted to the tiki cocktail revival.
Lychee cocktails can be difficult to balance, as lychees have a delicate flavor easily overpowered by other ingredients. The Lychee Lani recipe compensates for this by using the more-concentrated flavor of lychee syrup, and amplifying the floral notes with a touch of orgeat. The result is a heady, fragrant cocktail that brings to mind tropical flowers growing on the beach.
For the coconut rum, Modern Tiki suggests Clement Mahina Coco, a rhum agricole steeped with young, fresh coconut. It’s incredibly delicious, but currently quite difficult to find in most parts of the world. You can use whatever coconut rum or liqueur you like, but make sure it’s high-quality, and not overpoweringly sweet.