The whole point of LVM is that you CAN resize partitions, use multiple physical disks or partitions as one "logical" partition, etc. In order to utilize the free space you will need to create an additional partition using the free space.
Find out which disk the free space resides on using "fdisk -l", then do "fdisk /dev/hda" replacing hda with whichever disk is correct. Once a partition has been created using the free space we can now create a new physical volume:
Replace hda3 with whatever the name of the new partition is (available within "fdisk -l"). Now we will extend the Volume Group to the new physical volume like so:
vgextend /dev/VolGroup00 /dev/hda3
Where VolGroup00 is the name of whichever VG exists on your system (available by running "vgdisplay"). Where hda3 is the name of the new partition (again). Once the VG has been extended we can now extend the Logical Volume:
lvextend -L +20G /dev/VolGroup01/LogVol00
Where 20G is changed to the amount of free space available and VG and LV changed to their correct names. Once the Logical Volume has been extended we have to extend the ext4 filesystem within that LV:
Again, change the names to match your system. You can perform all of this on a running system..including the last command. Extending ext4 on a mounted partition works fine since early versions of the 2.6 kernel.