Ok! Just to be sure, I did it again...
In the LVM-Thin I have an 100.00g vm disk. Note that only about 6% are filled up.
lvs
  LV            VG  Attr       LSize   Pool Origin Data%  Meta%  Move Log Cpy%Sync Convert
  data          pve twi-aotz--  18.87g             31.33  1.86                           
  root          pve -wi-ao----   9.75g                                                   
  swap          pve -wi-ao----   4.00g                                                   
  vm-100-disk-0 pve Vwi-aotz-- 100.00g data        5.91 
No tried to use move_disk
cmd: qm move_disk 100 scsi0 VMS --format qcow2
(VMS is the Directory Storage)
Using this command to check the qcow2 file
cmd: watch -n 1 qemu-img info vm-100-disk-0.qcow2
Every 1.0s: qemu-img info vm-100-disk-0.qcow2                                                                     proxmox01: Wed Sep 30 11:02:02 2020
image: vm-100-disk-0.qcow2
file format: qcow2
virtual size: 100 GiB (107374182400 bytes)
disk size: 21.2 GiB
cluster_size: 65536
Format specific information:
    compat: 1.1
    compression type: zlib
    lazy refcounts: false
    refcount bits: 16
    corrupt: false
After a while, all space in /DATA, which is the Directory Storage are full.
df -h
Filesystem            Size  Used Avail Use% Mounted on
udev                  1.9G     0  1.9G   0% /dev
tmpfs                 394M  5.8M  388M   2% /run
/dev/mapper/pve-root  9.8G  2.5G  7.4G  25% /
tmpfs                 2.0G   52M  1.9G   3% /dev/shm
tmpfs                 5.0M     0  5.0M   0% /run/lock
tmpfs                 2.0G     0  2.0G   0% /sys/fs/cgroup
/dev/vdb1              40G   40G  316K 100% /DATA
/dev/fuse              30M   16K   30M   1% /etc/pve
tmpfs                 394M     0  394M   0% /run/user/0
and the image has almost 40G filled....
qemu-img info vm-100-disk-0.qcow2
image: vm-100-disk-0.qcow2
file format: qcow2
virtual size: 100 GiB (107374182400 bytes)
disk size: 39.9 GiB
cluster_size: 65536
Format specific information:
    compat: 1.1
    compression type: zlib
    lazy refcounts: false
    refcount bits: 16
    corrupt: false
And the command qm move_disk got error after a while:
qm move_disk 100 scsi0 VMS --format qcow2
create full clone of drive scsi0 (local-lvm:vm-100-disk-0)
Formatting '/DATA/images/100/vm-100-disk-0.qcow2', fmt=qcow2 cluster_size=65536 preallocation=metadata compression_type=zlib size=107374182400 lazy_refcounts=off refcount_bits=16
drive mirror is starting for drive-scsi0
drive-scsi0: transferred: 384827392 bytes remaining: 106989355008 bytes total: 107374182400 bytes progression: 0.36 % busy: 1 ready: 0
...
...
drive-scsi0: transferred: 42833281024 bytes remaining: 64541097984 bytes total: 107374379008 bytes progression: 39.89 % busy: 1 ready: 0
drive-scsi0: transferred: 42833281024 bytes remaining: 64541097984 bytes total: 107374379008 bytes progression: 39.89 % busy: 1 ready: 0
drive-scsi0: Cancelling block job
drive-scsi0: Done.
storage migration failed: mirroring error: drive-scsi0: mirroring has been cancelled
Then I tried to use qemu-img convert and everything works fine
qemu-img convert -O qcow2 /dev/pve/vm-100-disk-0 /DATA/images/100/vm-100-disk-0.qcow2
qemu-img info vm-100-disk-0.qcow2
image: vm-100-disk-0.qcow2
file format: qcow2
virtual size: 100 GiB (107374182400 bytes)
disk size: 6.01 GiB
cluster_size: 65536
Format specific information:
    compat: 1.1
    compression type: zlib
    lazy refcounts: false
    refcount bits: 16
    corrupt: false