Could not load file or assembly 'System.Data.SQLite'
System.Data.SQLite.dll is a mixed assembly, i.e. it contains both managed code and native code. Therefore a particular System.Data.SQLite.dll is either x86 or x64, but never both.
Update (courtesy J. Pablo Fernandez): Cassini, the development web server used by Visual Studio when you press F5 or click the green «play» button, is x86 only which means that even if your workstation is x64, you'll only be able to use the x86 version of System.Data.SQLite.dll.
An alternative is not to use Cassini but IIS7 which is properly x64.