The question "How can I get SQLITE to work with Unity" is an oft-asked question on the forums and the unity answers site.
Open Source =
The currently most well known SQLite implementation that is written in C# is found here: https://code.google.com/p/csharp-sqlite
It's really only for the windows (DeskTop,WinPhone, WinRT, and Silverlight) version of .NET though.
There is a paid-for unity-specific port on the asset store by OrangeTree: https://www.assetstore.unity3d.com/#/content/4334
There is a hacked version of the original port on github by [Opless] here: https://github.com/opless/csharp-sqlite
N.B. This is a hacky version to get working on mono (mac) which also happens to work to some degree on Unity. (28Nov2013)