Йодка прав. Вот процедура.
umount /home
e2fsck -f /dev/mapper/vg_oracle-lv_home
resize2fs /dev/mapper/vg_oracle-lv_home 20G
lvreduce -L 20G /dev/mapper/vg_oracle-lv_home
lvextend -l +100%FREE /dev/mapper/vg_oracle-lv_root
resize2fs /dev/mapper/vg_oracle-lv_root
mount /home