In order to use SQLite databases, you need to register a SQLite library using the Register Server dialog, after that, you can register databases for the given library.
Register a SQLite library
When selecting a SQLite library, Database Workbench will detect the version and display it to the right of the file selection box.
SQLite can use additional extensions to provide functionality beyond what SQLite offers by itself. You can use these for SQLite in Database Workbench as well, as per example above.