To extend a LVM volume that holds a ext4 filesystem can be tricky, as many tools only can process ext2 and ext3. But with the correct tools, this is straightforward.
Ensure e4fsprogs is installed.
Unmount the volume to be expaneded:
Extend the volume:
lvextend -L+10G /dev/mapper/VolGroup01-LogVol01
The option +10G extends the volume 10 GB. Another method would be to give a TOTAL desired size:
lvextend -L30G /dev/mapper/VolGroup01-LogVol01
Run a file system check:
e4fsck -f /dev/mapper/VolGroup01-LogVol01
Then extend the filesystem:
That is it.