The APIs are in Objective-C, not C++, so you’ll need to use Objective-C++ mode in your source files; the easiest way is to change the file suffix to “.mm”. This allows you to use Objective-C syntax in a C++ file (or vice versa.)
I am not familiar with JUCE, but perhaps the documentation has examples of calling other Objective-C APIs like Core Animation or AVFoundation? Using Couchbase Lite would be very similar.
I’ve done this sort of thing before, and it’s very straightforward once you get used to seeing the two syntaxes mixed together. It basically Just Works™.