I haven't used sqlite but I think this problem has been reported before.
Long-term solution: Please report this as a bug. At the very least there needs to be documentation on how to use sqlite on OS X.
Short-term solution: If you include the sqlite3dyn unit in your app, it looks like it will load the library dynamically rather than declaring it external. Then you can pass in the path to your .dylib in the InitialiseSQLite call. I'm not at my Mac right now, but I believe the sqlite.dylib is included on all Macs and will always be in /usr/lib - check that to make sure - my memory isn't what it used to be.
Thanks.
-Phil