To convert accdb to sqlite you need a special database management tools that support import of Access databases and write data to SQLite database file format. You can also use some exchange data formats and export accdb files into csv or xml, sql and then import it to SQLite database.
On Windows, Mac and Linux systems you can use Navicat database management tools like Navicat for SQLite or Navicat Premium to same purposes. Navicat software is available for Mac OS X too.
The ACCDB MDB Explorer, or Access Database Manager for Mac are able to transform Microsoft Access 2007/2010 database file (*.accdb file extension) to SQLite database file format (*.sqlite file extension).