Mounting encrypted LUKS partition from Live CD

Try this:

You need to Boot into a Live DVD/USB environment and open up a terminal window:

Press Applications --- Accessories--- Terminal

Install required packages using the following commands:

sudo apt-get update
sudo apt-get install lvm2 cryptsetup

Probe required module using the following command:

sudo modprobe dm-crypt

You find out which drive it was with the following command:

sudo fdisk -l

You must mount /dev/sda3 myvolume , You need to use cryptsetup:

sudo cryptsetup luksOpen /dev/sde3 myvolume

Now the device is accessible under /dev/mapper/myvolume

Scan for LVM volumes and choose the right volume group name that you are looking for:

sudo vgscan

Suppose it is system, activate that volume:

sudo vgchange -ay system

To find out your root volume, use the following command:

sudo lvs

Suppose it is root system you can mount it with the following command:

sudo mount /dev/system/root /mnt/

To work in volume use the following commands

sudo mount --bind /dev /mnt/dev 
sudo mount --bind /dev/pts /mnt/dev/pts
sudo mount --bind /proc /mnt/proc
sudo mount --bind /sys /mnt/sys
sudo chroot /mnt

You have LVM volumes inside the LUKS container. You should let the sytem know about them.

Run

sudo vgscan
sudo vgchange -a y

and then

mount /dev/mapper/ubuntu--vg-root /mnt/whateveryoulike