Sorry for not examining the issue enough earlier – I discovered that Themosis framework has nothing to do with my problem. Now, after further investigation I found out the what exactly causes the issue.
So what I discovered is that this plugin never works (seems to be working, but lightbox does not show up, as I described) when WordPress is served through PHP built-in web server (using “php -S” command).
I consider my problem solved, but this is something that in my opinion might be worth mentioning in documentation.