If you configure your database to use UTF-8 (I believe this is default for many installations; do PRAGMA encoding="UTF-8";
at schema creation time to be certain), this shouldn't be an issue.
If you send SQLite3 a set of characters encoded in UTF-8, it should have no problem dealing with it.
If Java has the ability to allow you to "toss a \u0039 into a string", I'd just use that, and ensure that when you try to place the string into the database, that you have the string convert to a UTF-8 byte encoding using whatever mechanism Java provides. I do not believe SQLite provides or needs to provide this for you.