I got a few questions and comments about how to actually include SQLite in a C# Metro style app. Since perhaps it wasn't clear in describing in my post, I thought a quick video might help demonstrate the steps to build and use SQLite in a C# Metro style app.
The video walks through actually building SQLite from the source (Visual Studio 2012 required.express is fine) and adding it to a C# Metro style app, create a database, populate with some data based on a class and databind the query to a ListView. The video references my OneNote notebook on the tools you need to download and build the SQLite source. It also demonstrates using the sqlite-net library from NuGet on interacting with SQLite in a C# application.