Unhappily it is not possible to have LiteSync as a loadable extension because there are many internal changes on the SQLite code implementing the required modules for replication.
But you may be able to use libspatialite with LiteSync. In this case we must load the extension when opening the database instead of using the
sqlite3_load_extension() or the
I have not tested libspatialite with LiteSync yet. You can do so using the modified SQLite shell from the download section.
Please inform if you have any problem.