LXC disk move

You can manually scp or rsync the disk from one location to another.

First shutdown your lxc container. Then rsync or scp it from one storage location to another - this location should already be mounted in PVE so you don't cause any issues.

You will need to know the name of your node, the vmID - normally 3 numbers.

Then edit the config file on one of your proxmox nodes:

pve/nodes/<node>/lxc/<vmID>.conf

There should be a line that reads:

rootfs: <old-location>:<vmID>/vm-<vmID>-disk.raw,size=XXG

Just change the old location to the new location.
 
In case you need to move a disk from one locally-attached storage (thin LV) to another locally-attached storage (thin LV), you could use the instructions from here:
unix <dot> stackexchange <dot> com/questions/214065/can-thin-lvs-be-moved-to-a-different-lvm-pool/218893#218893 .

Then, you can follow what nolag-hosting has mentioned in the post above to edit the container config file.