As you have found GParted can resize partitions, but not Logical Volumes. Extending the Logical Volume will have to be done from the command line. Steps (2) and (3) below represent the shortest possible sequence to query the required information and make the change. Run all commands as root, or prefixed with "sudo".
1) Show summary of the Volume Group and Logical Volumes.
2) Show the device name ("Filesystem" column) to the Logical Volume containing the root (/) file system. (Probably something like "/dev/mapper/ubuntu64--vg-root--lv").
3) Grow the Logical Volume to fill the Volume Group and grow the file system at the same time. (Replace "/dev/mapper/ubuntu64--vg-root--lv" with the actual device name found in step (2) above).
lvresize --resizefs --extents +100%FREE /dev/mapper/ubuntu64--vg-root--lv
This assumes you are using ext3 or ext4 root file system and want to grow it to fill all available space. It can be done online with the system up and running.
All of the above information can be found by searching the Internet for LVM documentation.