If you enable AJAX for RadLightBox, it will not refresh the entire page. I've isolated the sample from the Demo you've pointed out and enabled AJAX for it. Check out the following short video for demonstration: RadLightBox with AJAX enabled
I would like to note that having templates will always result in PostBacks which is described in the Lifecycle and Loading Content article, but you may enable AJAX to only do partial postbacks.
Here is the sample code snippet I've used for the Video demo: