No restart of the guest VM is required
lvextend /dev/lvm/domU.lan-var -L +5G
Extending logical volumedomU.lan-var to 7.00 GiB
Logical volume domU.com-var successfully resized
resize2fs /dev/xvdaX #(where X is a number)
resize2fs 1.42.5 (29-Jul-2012)
Filesystem at /dev/xvdaX is mounted on /var; on-line resizing required
old_desc_blocks = 1, new_desc_blocks = 1
Performing an on-line resize of /dev/xvdaX to 1835008 (4k) blocks.
The filesystem on /dev/xvdaX is now 1835008 blocks long.