Microsoft is now offering an official version of SQLite for Windows Phone, Windows Store, and .NET 4.5. The library is available as a Portable Class Library, so developers can use as a basis for their own portable libraries.
Internally the MS OpenTech library acts as a wrapper around the native implementations of SQLite that are available for ARM7, x86, and x64 platforms. (Though for .NET 4.5 only 32-bit mode is currently supported.)
The library is available as a NuGet package and the source code was released on CodePlex under the Apache 2 license. SQLite itself has been released in the public domain and has no licensing restrictions.
Microsoft Open Technologies is a subsidiary of Microsoft tasked with maintaining many of their open source projects. Besides SQLite they have a wide variety of projects related to MongoDB, Redis, Apache Cordova, CouchDB, and others. Most deal with either running these third-party technologies on Windows Azure or supporting Microsoft technologies on non-Microsoft platforms such as Eclipse.