This Script is an example for growing a Simple LVM inside a virtual machine, without downtime.

live_grow_lvm.sh

# Dont just copy and paste it!
# i am not responsible for any dataloss or other damage!

### grow the Disk in vSphere ###
# Just do it, there is no way to Script that

### rescan all SCSI Devices to detect the Change ###
for scsi in /sys/class/scsi_device/*/device/rescan; do
  echo 1 > $scsi
done

### delete and recreate the LVM Partition on /dev/sda1 to utilize all the free Space ###
### this assumes that /dev/sda only has one Partition (/dev/sda1), containing an LVM ###
parted --script /dev/sda \
  rm 1 \ # Deletes the First Partition
  mkpart primary 1 100% \ # recreates the first partition (1 is the Offset in MB)
  set 1 lvm on # enables lvm on the first partition

### rescan the Partition table ###
partprobe -s

### grow the "physical volume" on /dev/sda1 ###
pvresize -v /dev/sda1

#############################################################################
#### The Following needs to be "adjusted" depending on the actuall needs ####
#############################################################################

### grow the logical volume "var" by 90%FREE ###
lvresize -r -l +90%FREE /dev/mapper/vg_os-lv_var


### grow the logical volume "root" to fill up the remaining 10%FREE ###
lvresize -r -l +100%FREE /dev/mapper/vg_os-lv_var