@tuinstoel is correct, attaching to an SQLite database implicitly creates it if it does not exist.
SQLite also supports a command-line client that is more or less like MySQL's command shell, allowing you to issue ad hoc commands or run SQL scripts. See documentation here: http://www.sqlite.org/sqlite.html
Of course you need to change the Zend_Db adapter in your ZF application. ZF supports only an adapter to the PDO SQLite extension. SQLite doesn't support user/password credentials. Also since SQLite is an embedded database instead of client/server, the "host" parameter is meaningless.
$db = Zend_Db::factory("pdo_sqlite", array("dbname"=>"/path/to/mydatabase.db"));
One more caveat: when you get query results in associative-array format, some versions of SQLite insist on using "tablename.columnname" as the keys in the array, whereas other brands of database return keys as simply "columnname". There's an outstanding bug in ZF about this, to try to compensate and make SQLite behave consistently with the other adapters, but the bug is unresolved.