Grub2 recovery from live USB (LVM)
Boot from live usb. I use Debian 8. Open terminal and type
sudo su
Install LVM
apt-get install lvm2
List all logical volumes in all volume groups
lvscan
I have such a LVM structure
ACTIVE '/dev/v1/boot' [100.00 MiB] inherit
ACTIVE '/dev/v1/root' [10.00 GiB] inherit
ACTIVE '/dev/v1/tmp' [500.00 MiB] inherit
ACTIVE '/dev/v1/var' [30.00 GiB] inherit
Now mount devices to mnt folder
mount /dev/v1/root /mnt
mount /dev/v1/boot /mnt/boot
mount /dev/v1/var /mnt/var
mount --bind /dev /mnt/dev
mount --bind /proc /mnt/proc
mount --bind /sys /mnt/sys
Change root directory to mnt folder
chroot /mnt
Install and update Grub.
grub-install /dev/sda
update-grub
Note: Use command fdisk -l to determine which device contain Linux LVM. I have it /dev/sda