Aside from a few seconds to spin up a new PostgreSQL instance, it should not be any slower than SQLite. We have a wrapper [1] (forked from [2]) that starts a new PostgreSQL instance from Java unit tests. We have the same for MySQL [3]. This allows every developer to automatically run tests against the target database without needing to set anything up.
(The common alternative in Java is to use H2 or Derby, which are similar in concept to SQLite)