Suppose there is one LVM partition (except from /boot and maybe EFI), depending on the configuration of your virtual disk. As you choose LVM, you may proceed as follows:
Start gparted in the virtual machine, select the system disk, and create a new partition in the free space with type 'LVM'. You could also do this from the commandline with fdiskor gdisk, ifyou are used to. Remember the name of the newly created partition. For now say it's /dev/sda4.
Next, from commandline execute:
sudo pvcreate /dev/sda4 # to make the partition available for LVM
Now find out the name of your LVM volume group:
sudo vgdisplay
Remember the name of the volume group (say it is vg0). Then execute
sudo vgextend vg0 /dev/sda4
Again, find out the name of your logical volume
sudo lvdisplay
Say the volume's name is vg0-root. Then
sudo lvresize -r -l 100%VG vg0-root
should increase the logical volume vg0-rootto the possible maximum (option -l 100%VG) and resize the filesystem as well (option -r). The online resize of the (mounted) filesystem depends on your kernel; current kernels with ext2/3/4 filesystem support expansion of mounted filesystems.
An other solution would be to extend the partition itself with gparted, then use pvresize (see here, but for that you would have to boot Live Ubuntu from a CD or ISO, as you cannot increase a mounted partition through gparted.
If you could post some more information to your question (output of df, fdisk -l, pvdisplay, vgdisplay and lvdisplay), I could give you additional hints and correct my answer to fit your configuration.