The first thing you want to check and see is that your lightbox is set, under Gallery >> Other Options >> Lightbox Effects, and that it is not set to 'no lightbox'.
If it is set, then check and see that it's not a plugin or theme conflict. To troubleshoot, *deactivate all plugins (including NextGEN Gallery) > clear browser cache, and re-activate NextGEN Gallery only, reload your site and see if your galleries open. If it still not working, keeping only NextGEN Gallery activated, *temporarily switch your theme to a WordPress default theme like Twenty Twelve.
*there is a very low chance that by deactivating plugins/switching themes you may need to re-add some widgets or settings after re-activating or switching back to your theme.
If doing all the above, the lightbox is still not working, please read the below instructions:
NextGEN Gallery Lightbox Effects Not Working After Site Migration
If you have created a WordPress solution implementing NextGEN Gallery on a test, or development, server/site you may experience issues after migrating to the production site.
A typical issue we have seen are the Lightbox effects no longer working on the production site after testing fine on the development site. This is commonly due to the path not being correct for the “new” production site.
To correct this issue, please review all Lightbox effects “Advanced Settings” to insure the path to the necessary CSS and JS files are correct and resolve properly.
Look under: Gallery > Other Options > Lightbox Effects … (Show Advanced Settings)
Ideally the paths to the files referenced here will use the same path as the WordPress Installation. To insure the paths to these files is resolving correctly simply copy the file reference for the full path (from the http:// to the end of that line … either a CSS file or a JS file) and paste it into the address bar of your favorite Internet browser and surf to the file.
If a page of CSS, or JS as the case may be, is returned then the file path is correct; if a 404 / Page Not Found is returned then the file path is incorrect and needs to be amended to the correct path.
This path is relevant to your installation in most cases.
The most correct path will likely be along the lines of:
http://example.com/wp-content/plugins/nextgen-gallery/products/photocrati_nextgen/modules/... and also including the actual Lightbox CSS and/or JS as appropriate as part of the path. This is used for NextGEN Gallery and the Basic Lightbox Effects.
NextGEN Pro would use something more along these lines:
http://example.com/wp-content/plugins/nextgen-gallery-pro/modules/nextgen_pro_lightbox/static/ … followed by the appropriate CSS or JS file.
Running Reset Tool
What also helps after migrating your site from one location to the new location is running the NextGEN Reset Tool. This is located under Gallery > Other Options > Reset Options. Running this tool will not cause you to lose your galleries. What it does is clear any stored cache (i.e. old site URLs) and restores the global gallery settings back to default. So you will need to go back and re-adjust those settings after running the reset, but this tool may resolve the issue you're seeing with the lightbox.