If you have successfully upgraded the skin from Juicebox-Lite to Juicebox-Pro, then there should be no Lite 'jbcore' folder in the skin and jAlbum will have no option but to use the Pro 'jbcore' folder in the resulting gallery so there really ought to be no Lite 'jbcore' folder anywhere, except possibly already on your web server.
If you've ever used Juicebox-Lite and are upgrading a gallery to Juicebox-Pro then please check the following.
(1) Make sure when you upload your gallery to your web server that the Lite 'jbcore' folder is being overwritten with the Pro version. (It is possible that your FTP program might be set to not overwrite any existing files and folders.)
(2) Try clearing your browser's cache before reloading your gallery's web page to ensure that your browser is using the latest Pro files from your web server (instead of perhaps using older, cached Lite files).
If this does not help, then please post back with the URL to your gallery so that I can check it out for myself and hopefully help further.