How to extend a LVM volume
lvextend -L +2G <volume> -r
The -r flag automatically resizes the filesystem. If it's not provided, you need to manually run the resize2fs <volume> command.
The <volume> should be replaced with /dev/mapper/<volume group>-<volume name>. For example if I had a volume group called vg00 and the volume name would be var. The path would then be /dev/mapper/vg00-var
Verify Changes
You can run df -h and it should show the new amount. If it still shows the old one, you can try running the resize2fs <volume> command again.