Extend LVM logical volume without free space on the root partition.

Sometimes you can encounter such a problem when there is no free space on the root partition, so the volume group configuration backup cannot be created in /etc/lvm/archive directory.

$ lvextend --extents +100%FREE /dev/mapper/vg01-root

Couldn't create temporary archive name.

The solution is to disable the metadata backup.

$ lvextend --autobackup n --extents +100%FREE /dev/mapper/vg01-root

Size of logical volume vg01/root changed from 20 GiB (5120 extents) to <36.00 GiB (9215 extents).
WARNING: The metadata update is NOT backed up.
Logical volume vg01/root successfully resized.

So you extend LVM logical volume and resize the filesystem.

Additional notes

Sample metadata backup.

# cat /etc/lvm/archive/vgbackup_00001-687854914.vg 

# Generated by LVM2 version 2.03.07(2) (2019-11-30): Wed Feb 17 00:12:27 2021

contents = "Text Format Volume Group"
version = 1

description = "Created *before* executing 'lvcreate -n backup -l +100%FREE vgbackup'"

creation_host = "desktop"       # Linux desktop 5.8.0-43-generic #49-Ubuntu SMP Fri Feb 5 03:01:28 UTC 2021 x86_64
creation_time = 1613517147      # Wed Feb 17 00:12:27 2021

vgbackup {
        id = "TdI3hV-Nh3D-LFrL-pqrY-0T4K-HGfe-zSeqkI"
        seqno = 1
        format = "lvm2"                 # informational
        status = ["RESIZEABLE", "READ", "WRITE"]
        flags = []
        extent_size = 8192              # 4 Megabytes
        max_lv = 0
        max_pv = 0
        metadata_copies = 0

        physical_volumes {

                pv0 {
                        id = "9BAkBH-C2uE-k80V-1KfN-bjhm-HVmi-c4xoR9"
                        device = "/dev/mapper/sda_crypt"        # Hint only

                        status = ["ALLOCATABLE"]
                        flags = []
                        dev_size = 1953492400   # 931,498 Gigabytes
                        pe_start = 2048
                        pe_count = 238463       # 931,496 Gigabytes
                }
        }
}