The library databases are subscription resources only available to Lone Star College students and employees. When you click on one of these database links from off-campus, you'll be redirected to a page asking you to enter your 14-digit library barcode. Once you've provided your credentials, the site will automatically finish taking you to the database.
They are very exciting resources. LSC-Online users should look for the link that will let you get access by signing in with your regular myLoneStar username and password. However! If you're trying to access a campus-specific item (it'll be labeled as such), you'll have to use your barcode.