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