Yes. The Database Query Tool allows developers to interface with SQLite interactively via SQL commands. It can be downloaded at http://code.google.com/apis/gears/tools.html. Simply copy the "dbquery.html" file to your server directory and visit the URL in your browser, and you can start issuing SQL commands to the embedded SQLite. There is also a similar third party tool, called Gears In Motion which is very good.
If you desire to check the contents of localserver.db (the database for LocalServer) then it is suggested that you use a SQLite management client. A list of them can be found here.