Execute:

vgscan
vgchange -a y

as root and all the partitions should have devices created in the form /dev/volumegroup/logicalvolume, which you can then mount in the usual way:

mount /dev/volumegroup/logicalvolume /mnt/somewhere

1. Boot from a live disk or USB.

2. Search for these tools: lvm2. If not found then install it.

sudo apt install lvm2

/proc/misc: No entry for device-mapper found
Is device-mapper driver missing from kernel?

modprobe dm-mod

3. Make sure the harddisk is recognised.

fdisk -lu

4. Run pvscan to scan all disks for physical volume. This is to make sure your LVM harddisk is detected by Ubuntu.

pvscan

returns

PV /dev/sda2 VG VolGroup00 lvm2 [74.41 GB / 32.00 MB free]
Total: 1 [74.41 GB] / in use: 1 [74.41 GB] / in no VG: 0 [0 ]

5. Run vgscan to scan disks for volume groups.

vgscan

returns

Reading all physical volumes. This may take a while...
Found volume group "VolGroup00" using metadata type lvm2

6. Activate all volume groups available.

vgchange -a y

returns

2 logical volume(s) in volume group "VolGroup00" now active

7. Run lvscan to scan all disks for logical volume. You can see partitions inside the hard disk now active.

lvscan

returns

ACTIVE '/dev/VolGroup00/LogVol00' [72.44 GB] inherit
ACTIVE '/dev/VolGroup00/LogVol01' [1.94 GB] inherit

8. Mount the partition to any directory you want, usually to /mnt

mount /dev/VolGroup00/LogVol00 /mnt

9. Access the partition in the /mnt directory as required.

Script

DISK=mydisk
 
lvdisplay | grep $DISK | grep "LV Path" | sed 's/.* //g'
LV_DISK=$(lvdisplay | grep $DISK | grep "LV Path" | sed 's/.* //g')
 
fdisk -l $LV_DISK
fdisk -lu $LV_DISK | sed -n '/lv[0-9]p[1-3]/ p' | grep p1 | awk '{print $2}'
 
OFFSET=$(fdisk -lu $LV_DISK | sed -n '/lv[0-9]p[1-3]/ p' | grep p1 | awk '{print $2}')
OFFSET=$((OFFSET * 512))
 
MOUNT=/mnt/$DISK
mkdir -p $MOUNT
mount -o loop,offset=$OFFSET $LV_DISK $MOUNT