Solution 1:

Ok, so after much toiling I finally figured out how to do it. And again, gparted cannot be used. Firstly, you should expand the size of the disk in VMWare Workstation. Boot into a livecd and open a root terminal:

We need to create a new primary partition of type LVM out of the free unused space.

#fdisk /dev/sda
#Command (m for help): n
#Command (m for help): p
#Command (m for help): 3
#Command (m for help): w

Reboot the vm into the live cd again

Create the phyisical volume:

#pvcreate /dev/sda3

Add the new volumn to the group:

#vgextend ubuntu /dev/sda3

Find out how much free space you want to expand to

#vgdisplay

Check what "Free PE/Size" equals and use that value in the next command

Extend the lvm and grow the file system into the new space

#e2fsck -f /dev/ubuntu/root
#lvextend -L +12.6G /dev/ubuntu/root
#resize2fs /dev/ubuntu/root

Done!

Solution 2:

Back up your machine. Boot the system with GParted and grow the partition. Apply the changes.

Here is a video.