I want to add a Close button within the lightbox that behaves the same way as the 'X' icon at the upper right of the lightbox frame. I don't want to refresh the underlying page due to some ajax sorting and filtering that may have been applied.

I am using the lightbox to display another HTML page, if that matters...

Hello,

You ca do this by adding such a button/link in the page you are showing within the lightbox.
Then select the button go to Tag Inspector > Behaviors > Control DMXzone Lighbox and use the settings as on this screenshot: