How to expand a btrfs Storage pool on a dedicated LVM logical volume?

I have a btrfs storage pool which lives on a dedicated partition (an LVM logical volume tp be precise) which apparently ran out of space.

  1. how can I check the free/used space on a storage pool
  2. will the storage pool enlarge it’s capacity automatically once I add space to the Logical Volume?

obviously lxc storage info [pool_name] provides that sort of information

I think it won’t and you’ll have to extend the filesystem after the LV has been extended.
However I don’t really know how to do that.

You can locate a btrfs filesystem

$ sudo btrfs fi show
[sudo] password for [user]: 
Label: 'default'  uuid: d9320138-3142-4e44-93bd-a0e9ccbfef4a
	Total devices 1 FS bytes used 18.99GiB
	devid    1 size 20.64GiB used 20.64GiB path /dev/mapper/vg0-lxdPool

but as there is no mountpoint you can not maniupilate it with common btrfs fi ... /path/to/fi commands cause it throws a not a btrfs filesystem: /dev/mapper/vg0-lxdPool error at you. I guess this is due to the fact lxd seems to disguise the mount point of dedicated partitions used for pools somehow to the hosts OS. Is there anyway out of this?