ReStore for Dolphin currently only supports database connections via ODBC so you'd need to ensure the SQLite ODBC driver is installed on a target machine.
You can avoid the need to set up an ODBC datasource by specifying a connectString rather than a dsn, for example:
aReStore connectString: 'DRIVER=SQLite3 ODBC Driver;Database=c:\mydb.db'
Porting the SQLite native client from Pharo is on my to-do list so will hopefully happen at some point.
Hope this helps,