You will need to shrink your LVM root volume to be able to create an additional volume to be mounted separately. The process requires that you boot into rescue mode using a startup CD/DVD and drop into a shell without mounting the root partition.
vgchange -a y
fsck -f /dev/vg_vm025/lv_root
resize2fs /dev/vg_vm025/lv_root 100G
lvresize -L -100G /dev/vg_vm025/lv_root
lvcreate -L 20G -n lv_home vg_vm025
You then have a new volume named "lv_home" that you can mount.
So yes, it is possible, but the process is rather complex. If you are not familiar with the concepts and administration of LVM I suggest to reinstall the system and customize the installation process. You can find info in the standard installation guide.