Processing SQLite files using ArcGIS Desktop?

You can install the Open Source ArcGIS OGR Workspace plugin from AmigoCloud that will give ArcMap read access to spatialite and a whole bunch of other formats. It is free. Let me know if you want to test the binaries - I already have some people doing that with success. They only work with 10.1 at the moment since that is the only ArcGIS version I have access to. It should compile fine on 9.3 though.

My understanding is that to do this using ArcGIS Desktop 9.3 (or 10.0 or 10.1) the simplest, but expensive, option would be to use the Data Interoperability extension.

However, using ArcGIS Desktop 10.2 (or later) with no extensions ...

You can connect from ArcGIS to an SQLite database to create maps and perform spatial analysis on your data.

You connect directly to the SQLite database file from your ArcGIS client.

To store and work with spatial data, you must have either the Esri ST_Geometry type or SpatiaLite installed in your database. You can use the CreateSQLiteDatabase ArcPy function to create an SQLite database with either of these spatial data types.