If we are to attribute this drink to the town in Scotland by the same name, it would be pronounced "Coo-ros".
There's not much out there with this rather strange name, so its not a bad bet that this drink was named after the town, or possibly after a patron from Culross that the Harry Craddock era Savoy Hotel Bar honored in the naming of this one.
It does not seem very Scottish in nature, but Culross is a coastal town, and the maritime influenced Scots have been known to enjoy their fair share of rum.
At any rate, this appears first in the Savoy Cocktail book in 1930 with the following instructions:
If you are unable to use Havana Club, go for Flor de Caña Extra Dry 4 year, a rum that is much closer in character to the original Cuban Bacardi than the modern Barcardi Dry made in Puerto Rico.
The closest thing that we have on the market today to Kina Lillet, is Cocchi Americano (rather than Lillet Blanc.) It is bolder and more spice forward than Lillet Blanc. They are both traditional white aperitif wines, Lillet coming from France and the Cocchi from Italy, and their histories are intertwined.
For some recipes they can be used interchangeably. For other recipes, one works well where the other can be glaringly off. Since this one called for Kina Lillet by name, Cocchi Americano seemed the obvious choice.
This is an interesting mix, you have the Cocchi and lemon juice on side, providing dry and sour flavors. On the other side you have the light, sweet rum and the big flavored Apy.
If you have been able to secure a bottle of Marie Brizard Apry (it can be a challenge to locate) - this is a nice way to use it as it works very well here. It is just sweet enough to make up for the lack of sugar or simple syrup, and its apricot fruit flavor works great with the other flavors here making for a sweet, yet oddly dry mix.