Ok- First, if you add a second hard disk to a existing volume group, you take a big risk: any disks failure from that volume group will make all logical volume go unavailable. You will also not have any of the added benefit such as stripping. You would have to add a raid array (+2 drives minium, for raid 5), to see at least some kind of benefit.
The only reason why you would want to add a drive to an existing volume group is if you would like to extend a specific partition. In the present case, you want to add a new one (give all the space to /opt/splunk/lib).
I would suggest you do the following:
Identify the new HD (for the rest of the walkthrough, I'll take for granted you found /dev/sdb):
Create a new partition on the drive (could also use the whole device and jump that step)
fdisk /dev/sdb ;
New, Primary, ID:1, from Start, to End ;
Create a new physical volume
Create a new volume group
vgcreate splunk /dev/sdb1
Create a new logical volume (size 100gb, named splunk_lib, from the splunk volume group)
lvcreate -l 100g -n splunk_lib splunk
Create a file system on the new logical volume
Create a mount point & Mount the new filesystem
mount /dev/splunk/splunk_lib /tmp/splunk_lib
Stop splunk, sync lib directory
rsync -avz /opt/splunk/lib/* /tmp/splunk_lib/.
Unmount, move and remount
umount /tmp/splunk_lib ;
mv /opt/splunk/lib /opt/splunk/old-lib;
mkdir /opt/splunk/lib ;
mount /dev/splunk/splunk_lib /opt/splunk/lib
Don't forget to add it to /etc/fstab (to be up at next reboot)
vi /etc/fstab or