I installed the VSIX for SQLite and noticed that it is a native DLL to be used in Windows Store 8.1 C++ apps. It is not for managed C# projects.
The current NuGet package for SQLite from what seems to be the 'official' SQLite team is only working for .NET 4.5, if you try to install it, it will error saying it does not support .NET 4.51.
There is also the NuGet package SQLite-net, which works for .NET Windows Store apps. All you need to add is the SQLite using statement.
You will need this NuGet package as it is the managed wrapper for the SQLite, without you will not be able to properly reference the right DLL for SQLite.
Here is the link to the project information from that NuGet package. SQLite Runtime Support
Here is an article on how to use SQLite with Windows Store apps in VS2012 but it should still all apply: