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.
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