I was able to build Massive.Sqlite on Mono 2.6.10 and get selects, inserts, updates and deletes working. I haven't tried anything else yet. You can look at the examples on how to do that stuff here:
https://github.com/robconery/massive
A couple points to note are that you have to change two lines so they work with Mono.Data.Sqlite instead of System.Data.Sqlite.
Replace
using System.Data.SQLite;
with
using Mono.Data.SQLite;
I also had to change line 128 from:
var _providerName = "System.Data.SQLite";
to
var _providerName = "Mono.Data.SQLite";
If you are using MonoDevelop and create a new project you'll need to set it to use the .NET 4 profile and then add the following references to your project:
Microsoft.CSharp
Mono.Data.Sqlite
System.Configuration