Sorry for digging up this old thread but I came across this issue a few days ago when I found out that Proxmox refused to migrate VMs that are stored on a local LVM.
I don't know if this behavior is intended but I've found a workaround that even makes it possible to do a kind of live migration on LVM based local storage with only some seconds of downtime.
I created a bash script that takes care of every step neccessary to migrate a VM from one cluster node to another while keeping it online as long as possible.
Basically this boils down to the following steps:
1.) lookup VMs Harddisks
2.) background sync them to the target node
3.) pause node
4.) move node to target
5.) unpause it
6.) done!
More detailed description of my script is available on my Website (sorry still building it up...) here:
https://ischmidt.info/pages/home/it/pveulm.sh.php
It is called pveulm. (Proxmox virtual environment unsynced live migration)
I attached the script to this post as a .txt file. Of course it is also available under the above site and there you will always find the newest version. (Maybe i will move to a GitHub project later on)
Feel free to use it, share it, modify it. Please let me know if you have suggestions, improvements etc.
I hope this helps, saving some people a lot of time...
EDIT: Found a dangerous BUG!
Variable $_snapname was not correctly set when handling more than one virtual Disk. This leads to data corruption when a VM with multiple disks is migrated. - FIXED!