Is that possible to backup MongoDB sharded cluster without LVM or mongodump?
The LVM method works they way it does because snapshots are really fast, and the outage is really small and easily within the replication-log window. Using file-copy methods extends how long the replica-member is not replicating, so how long you can take to back up is constrained by the maximum replication-log allowed on the master node.

Secondly, snapshotting takes a point-in-time backup of all files at the same time which improves the consistency of the backup. For a file-copy style backup the files will be read sequentially, so the use of db.fsyncLock() is massively important; if you don't, the chance you're backing up inconsistent files is really high. It's the use of db.fsyncLock() that starts causing the replica to fall behind and the replica-log to increase on master.