I would assume this implies that LocalDB is replacing SQL Server Express.
Your assumption is incorrect. Keep reading the article you linked...
LocalDB is not a replacement for SQL Server Express -- it is an addition to SQL Server Express lineup. While LocalDB is meant for developers, the regular SQL Server Express will continue to exist as a free SQL Server edition, fully compatible with and easily upgradeable to higher SQL Server editions.
You would still use SQL Server Express or a higher version of SQL Server for production use. Or better yet, abstract your application from the database in such a way that you could use any server (MySQL, Oracle, etc.)