With LiteSync you don't need to worry about wifi range, pressing button or selecting which rows to update. All is done automatically. Including updated rows, deleted ones, new created tables, indexes, and so on...
I suggest you to make a test with the modified SQLite shell and check by yourself. You can also use the sample project for Android Studio available on the download page.
Just notice that with the current version you need to start with empty databases on both sides and then create the tables and insert the rows on one of the nodes. These changes will be replicated to the other nodes. Once that migration step is done, all new changes on any node will be synchronized to the others.
Data migration (and merging) from existing databases will be available very soon, as well as better quality videos.
Please inform if you have any problem.