The concurrency protection offered by SQLite depends on file locks to protect against data loss. This model allows multiple database connections to access a database at the same time, but the whole database file must be locked in an exclusive mode to make any changes. As a result, write transactions are serialized across all database connections, limiting the overall transaction rate. (link)
Depending on the size and complexity of your updates, SQLite might be able to handle a few hundred transactions per minute from different processes or threads. (link)