Unfortunately, what you are looking to do might not be possible. When a gallery is expanded to fill either the browser window or the entire screen, only the gallery itself (essentially the 'juicebox-container' <div>) is displayed. The code which handles the gallery expansion is buried deep within the 'juicebox.js' JavaScript file which is obfuscated and cannot be modified.

The only way to do something like this would be to set expandInNewPage="TRUE" (in the General Options section), a Juicebox-Pro option which is not supported by Juicebox-Lite.

This will force the gallery to be expanded in a new web page (instead of on top of the embedding page or triggering the Fullscreen API to cover the entire screen). The web page that is used when the gallery is expanded in this way is the 'full.html' file within the gallery's 'jbcore' folder.
You could then modify this HTML file to change the gallery's dimensions (reduce the size of the gallery from 100% x 100% to allow room for your own custom content) and add your own HTML code in a custom <div> alongside the gallery.

I expect that this should work but please note that this is untested and modification of the 'full.html' file is not officially supported so you would do so at your own risk. (You may run into unforeseen problems that might need to be tackled along the way.) Also, there is no way for the 'full.html' file to be used in conjunction with the Fullscreen API so when the gallery is expanded, it will fill only the browser window and not the entire screen.