Considering that DFS Replication is oriented towards files and folders:
DFS Replication is an efficient, multiple-master replication engine
  that you can use to keep folders synchronized between servers across
  limited bandwidth network connections.
I would probably try to avoid it if you care about consistency and keeping all your data, as stated by the SQLite backup documentation: 
Historically, backups (copies) of SQLite databases have been created
  using the following method:
- Establish a shared lock on the database file using the SQLite API (i.e. the shell tool).
- Copy the database file using an external tool (for example the unix 'cp' utility or the DOS 'copy' command).
- Relinquish the shared lock on the database file obtained in step 1. 
This procedure works well in many scenarios and is usually very fast.
  However, this technique has the following shortcomings:
- Any database clients wishing to write to the database file while a backup is being created must wait until the shared lock is relinquished.
- It cannot be used to copy data to or from in-memory databases.
- If a power failure or operating system failure occurs while copying the database file the backup database may be corrupted
  following system recovery.
In the case of DFS, it wouldn't even lock the database prior to copying.
I think your best bet would be to use some kind of hot replication, you might want to use the SQLite Online Backup API, you could check this tutorial on creating a hot backup with the Online Backup API. 
Or if you want something simpler, you might try with SymmetricDS, an open source database replication system, compatible with SQLite.
There are other options (like litereplicator.io), but this one went closed source and is limited to old SQLite versions and ~50MB size databases
ps. I would probably move away from SQLite if you really need HA, replication or this kind of features. Depending on your programming language of choice, most probably, you already have the DB layer abstracted and you could use MySQL or PosgreSQL.