Is there a free software addition to SQLite available for data-replication?
Berkeley DB's SQL API is completely SQLite compatible and offers HA/replication for high availability. The combination of SQLite's easy-of-use and Berkeley DB's scalability and reliability are a great combination. 

Disclaimer: I'm the Product Manager for Berkeley DB, so I'm a little biased. However, one of the main benefits of adding the SQLite API to Berkeley DB is that SQLite applications can now have HA/replication for mission-critical, highly available applications.