When you met root space is too big and you want to reduce them.

reboot your system to an rescue mode and skip to chroot mode

then do

#lvm pvscan

#lvm vgscan

#lvm lvscan

#e2fsck -f /dev/[volgroupname]/[lvname]

#resize2fs /dev/[volgroupname]/[lvname] [volume spcace]

#lvm lvreduce -L [volume spcace] /dev/[volgroupname]/[lvname]