Hello!
There's two ways you can make Iavra's localization plugin work with TAA_BookMenu. The first one is to create a books.json file (or use the Plugin Manager) and set each book field as a localization key (Iavra's plugin uses #{{key}} by default, if I'm not mistaken). But that means you'll basically duplicate the entire library in yet another file.
The second way is the built-in integration I did with both plugins. To use it, set the datasource type to "Localization File" and point the file to one of your localization files. Then simply put the whole books.json structure inside your localization file (and have it on each language file with the same structure). Be sure to set the Localization Escape Code to the same key used by Iavra's plugin. And that's it!
Basically, you won't need the books.json, because its contents will be replicated into each language file (don't translate the object keys, just the texts).
I'm not sure if my explanation wasn't a bit confusing, so let me know if you still have questions.