You don't really want to upgrade the system version of SQLite on Mac OS X. The reason is that all Mac OS X software is qualified against the versions of the packages that it includes, as built by Apple's build process. Installing a different version of a package, or even building the same version yourself but doing so slightly differently than Apple does, may result in a system that behaves unexpectedly.
Finally, if you embed a newer version of SQLite — or any Open Source library or framework included with Mac OS X — into your own application, you should be sure to integrate the Darwin changes for it from Apple's public source site. That way you can be sure you'll get as close to the same behavior as possible from the library you've built yourself as the version Apple ships, which is especially important when it comes to functionality like file locking in databases.