Hi,
I don’t think this lightbox supports an html page inside the lightbox. I have not tried all the supported lightboxes in Responsive Lightbox, I just tested with default SwipeBox. But you could try them and see.
A nicepackage that supports HTML inside the lightbox is Floatbox JS. The author, Byron McGregor has released it for FREE under MIT License. Previously a license was $20.
It supports a lot of inner-elements besides images: html, pdf, video and maybe more. See docs.
Floatbox does not have wordpress plugin last time I checked, but can be easily loaded in a child theme. Floatboox supports images added dynamically via ajax/javascript after page load with fbactivate() which is not typical of a lot of lightboxes and if you load content after page is initially rendered, it is the only choice I know of.
Good Luck!