Is it possible to use SQLite as a client-server database?
SQLite is an embedded database and it is not intended to be used as a client/server DB. If you really want to, you can use SQLitening.

What SQLitening is


  SQLitening is a client/server implementation of the very popular SQLite database.
  
  SQLitening is a programmer's library in standard Win32 DLL form. It is installed as a standard Windows Service. In addition to client/server mode, the library allows the programmer to also access SQLite databases in local mode. In either mode (local or client/server), the database is extremely fast and robust.
   -- Source: http://www.planetsquires.com/sqlite_client_server.htm