On a Mac, all you should need to do is extract the 'juicebox_lite_1.5.0.zip' file, go inside the 'juicebox_lite_1.5.0/adobe-lightroom-plugin/' folder and double-click the 'juicebox_lite.lrwebengine' package.
If this does not work, then it might be worthwhile uninstalling and then reinstalling Adobe Lightroom to see if this helps (although the manual method of copying the 'juicebox_lite.lrwebengine' package to the 'Web Galleries' folder should also work fine).
Also, please make sure that you have Adobe Lightroom v4 or later installed. The 'juicebox_lite.lrwebengine' plugin will not work with Adobe Lightroom v3 or earlier.
2. I am on a Mac, yes, and; 'Users/username/Library/Application Support/Adobe/Lightroom/Web Galleries/' does not exist
If you cannot find Adobe Lightroom's 'Web Galleries' folder on your computer, then please try the suggestion from my post above:
Open Lightroom
Go to 'Edit -> Preferences...' (from the drop-down menu at the top)
Select the 'Presets' tab
Click the 'Show Lightroom Presets Folder...' button
Navigate inside the 'Lightroom' folder in the file explorer window that pops up
Now navigate inside the 'Web Galleries' folder
This is the folder that you should copy and paste the 'juicebox_lite.lrwebengine' package to (when installing the plugin manually if double-clicking the 'juicebox_lite.lrwebengine' package does not work).
If you do not have a 'Web Galleries' folder (although it should exist by default after installing Lightroom), then try creating it manually in your 'Users/username/Library/Application Support/Adobe/Lightroom/' directory.
3. Looking into the package content? Doesn't show anything neither.
There should be no need to look inside the package (although it seems strange that you do not see anything inside it).
To install the plugin to Adobe Lightroom, either double-click the 'juicebox_lite.lrwebengine' package or, if this does not work, copy and paste the 'juicebox_lite.lrwebengine' package to the 'Web Galleries' folder (see above).
So Any idea where this """juicebox_lite.lrwebengine""" is hidden? Does it exist, even?
The 'juicebox_lite.lrwebengine' package is bundled within the Juicebox-Lite zip file.
Extract the 'juicebox_lite_1.5.0.zip' file and you'll find the 'juicebox_lite.lrwebengine' package in this location: juicebox_lite_1.5.0/adobe-lightroom-plugin/juicebox_lite.lrwebengine
4. Looking into the Libraries (several possible locations)? Nothing there neither.
The only location that the plugin should be installed to is 'Users/username/Library/Application Support/Adobe/Lightroom/Web Galleries/'.
I noticed you mention 'juicebox_pro.lrwebengine', but PRO wasn't my issue. Lite is. and This is the forum for Lite. No?
Sorry. There was an instance of 'juicebox_pro.lrwebengine' rather than 'juicebox_lite.lrwebengine' in my post above (which I have since corrected).
I hope these notes help you to successfully install the plugin.
Edit:
Incidentally, the Lightroom plugin was first bundled into the Juicebox-Lite zip file in v1.4.3.
If you have a version prior to v1.4.3, you will not find the 'juicebox_lite.lrwebengine' package inside the Juicebox-Lite zip file.
You can download the current version of Juicebox-Lite (v1.5.0) from the download page here.