actually the plugin has a style that you can choose to have descriptions under the pictures, it's called "LightBox WITH labels" - it uses the labels you set in the gallery.
Hope I understood well the question, extracting the images "description" fields and using them as labels is not at all supported at present, even though it might be an interesting feature to be added.
Unfortunately the "LightBox WITH labels" worked fine on the default theme in WP 3.6, it seem not to work on the new default theme in WP 3.7 and in many other.
I haven't had much feedback about this style so far, that's because the issue was a bit left behind.
Please, enable te "LightBox WITH labels" style on a post/page where you have the gallery, then post its URL.
This way, I can see what I can do.