Yes i had this same problem too — all fine now for me. Curious did u minify js files too or just css files? The conflict is usually because the ordering of files is going in wrong. You may want to set your minify to “Manual”, go to the Minify settings, select the wizard to populate the discovered files, and then go about reshuffling them around to get the right order.
However, if it is just css files then its possible one of the required css files for the lightbox (and its required classes) is missing. Not sure if you have done debugging before but if u have firebug installed in your browser you could check to see what is going on and get it resolved fairly quickly.
For me, i disabled the plugin and used firebug to see what css/js files were being included and their specific orders, taking note of any inlined js files that were depenedant on said css/js files. With that in hand you can renable w3tc and see where the minified file(s) were included and which js/css files were not included (and their order).
First thing i would do though is check firebug to see if any js errors exist in the console tab. If so ill bet good money jquery is placed incorrectly.
Anyway, if you need assistance, just provide me your domain. I wish there was a way for me to see both the minified mode and non-minified…with that id be able to tell you what is wrong immediately ?? — nonetheless, if u have the minified mode enabled ill be happy to check for the (likely) js error on your page.