Yes, the Lucid Player can run from a Hard Drive, USB, CD\DVD or a web server. If the key has been deployed via the Lucid Mobile Platform, then it can also run from Android and iOS devices.
Note: If a key author has posted a key via their web server, not as a downloadable file, then the key is set to run from the website. That is it won’t run off your hard drive or run while you don’t have an internet connection.
The key author may have also connected some or all of the keys media to a website(s), even though it maybe running from your hard hard, for example. In this case the key will operate from the hard drive without an internet connection, but the Internet based media will fail to load if you don’t have an Internet connection. If in doubt consult the key author on their keys configuration and requirements.