In any situation where images come from different source than native WordPress post you have to apply lightbox manually:
for single images:
<a href="full size image url" title="the title of the image" data-rel="lightbox">image thumbnail or text</a>
for galleries
<a href="full size image url" title="the title of the image" data-rel="lightbox-gallery-1">image thumbnail or text</a>
If you want to create multiple galleries displayed separately just modify the data-rel to lightbox-gallery-2 then 3,4,5 etc.
It does not really matter where these images or galleries come from or where are displayed on page – with the data-rel you can control how Responsive Lightbox handles it.