Which is the most performant way to copy a number of SQL Server tables to a readonly SQLite database?
I have successfully used SQL Server Integration Services (SSIS) to setup a job to "archive" data to SQLite databases. A quick way to build a SSIS job, is to do a Task->Export Data task. At the very end you will see a checkbox on the top left asking you if you want to save this as a SSIS job.

Make sure that you have installed the SQLite provider from http://sqlite.phxsoftware.com/

You can schedule this SSIS package once it is saved.