If you're using LVM for the primary partition you can always add another disk to the pool and then extend into it. Given you're using CentOS I would assume that the system was setup so that you have an LVM partition providing your storage and then their are logical volumes coming from LVM for /home
and /
.
Example
Here on this CentOS 6.x system I have the following physical volumes being included into LVM.
$ sudo -i
$ pvs
PV VG Fmt Attr PSize PFree
/dev/sda2 VolGroup00 lvm2 a-- 465.66G 0
The HDD /dev/sda2
is part of a single volume group:
$ vgs
VG #PV #LV #SN Attr VSize VFree
VolGroup00 1 3 0 wz--n- 465.66G 0
The logical volumes are as follows:
$ lvs
LV VG Attr LSize Origin Snap% Move Log Copy% Convert
LogVol00 VolGroup00 -wi-ao 442.19G
LogVol01 VolGroup00 -wi-ao 13.69G
LogVol02 VolGroup00 -wi-a- 9.78G
These logical volumes get mounted like so:
$ mount
/dev/mapper/VolGroup00-LogVol00 on / type ext3 (rw)
So you could add another disk to the volume group and then make use of it in which ever logical volume needs the space.
Diagram

The above, hopefully, illustrates how LVM architecturally works. Often times, people will create LVM volume groups which sit on top of RAID arrays. This gives you the ability to expand a filesystem using LVM but with the protection offered through the use of a RAID array for redundancy purposes.
So you could add another physical volume to the VG (volume group). This new physical volume would then show up as new space which could then be allocated to one of the LG's (logical volumes).
Migrating to RAID
I would suggest setting up the RAID along side your existing HDD. You can setup a RAID array as RAID1 (then degrade it by only adding 1 HDD to it.)
Once the RAID array is setup, I'd put LVM on top of it as discussed above, and then migrate the data from the existing HDD to the LVM topped RAID1 array.
Once the data has been migrated in, you can then bring the original disk into the RAID1 array and resync it.
For the nitty gritty details I often refer to this HowtoForge article, titled: How To Set Up Software RAID1 On A Running LVM System (Incl. GRUB2 Configuration) (Ubuntu 10.04). Don't let the reference to Ubuntu scare you away, most of the steps are identical and I find the level of details in this particular article crucial to understanding what you're actually doing for the various steps when migrating to a LVM + RAID1 setup.
References