If you want to ask for suggestions for plugins, post in the "Using jQuery Plugins" section of the forum.
Search the forum first, because the question almost certainly has come up before. In fact, I know it has. Search, and see what others have suggested in the past.
Neither jQuery UI nor jQuery Mobile have a lightbox feature. So, you strike-out on "by using any free jQuery framework".
There are dozens of lightboxes. Some/most of them require jQuery. Most/all of the tolerate jQuery. Many are written as jQuery plugins. Some can be used without jQuery, but include an optional jQuery plugin. You don't NEED a jQuery plugin, but it is more convenient if the lightbox script you choose is a jQuery plugin.
Dozens of choices. Pick one that you like.
