I only had a chance to take a quick look at it, i'll have to take a look at the webpart logic that runs it, however what would probably be recommended is you diverge from using that built in lightbox as depends on reloading the page (it generates a link to the current page with some URL parameters that then i believe will 'trigger' a larger view of it), and instead use a repeater and your own jQuery plugin. It will be a lot more flexible as you can pick and configure as you want.
Fancybox is a great plugin for example, just include the javascript and use a Repeater to display the file objects you want and render them to match the HTML format required.
http://fancyapps.com/fancybox/3/docs/
I'll hopefully get back to you sometime early next week when i can get back at the office to take a look.