tests/test_framework/phpbb_database_test_case.php does not handle SQLite databases very well. It doesn't open the database correctly, the DSN is wrong.
Some of the CREATE queries can lead to issues, see: http://bugs.php.net/bug.php?id=51492
The PDO connection uses sqlite3, phpBB's DBAL only supports sqlite2. The two are not compatible, therefore phpBB cannot open the database.
PHPUnit does not support sqlite2. I have created a patch to add support and sent a pull request: http://github.com/evil3/phpunit/compare/3.4...sqlite2-mapping
You can use my fork of PHPUnit to run the tests. Just do: