1. You create the target on the target volume group:

core:osx# lvcreate -L100G -n MacPool100Glv bkupvg
  Logical volume "MacPool100Glv" created

2. Have a visual of what you have to do. We have below the target (/dev/bkupvg/MacPool100Glv) and source (/dev/datavg/MacPool100Glv):

core:osx# lvscan
  ACTIVE            '/dev/bkupvg/corelv' [250.00 GB] inherit
  ACTIVE            '/dev/bkupvg/MacPool350Glv' [350.00 GB] inherit
  ACTIVE            '/dev/bkupvg/MacPool100Glv' [100.00 GB] inherit
  ACTIVE            '/dev/datavg/mylv' [2.10 GB] inherit
  ACTIVE            '/dev/datavg/weblv' [72.00 GB] inherit
  ACTIVE            '/dev/datavg/maillv' [1.00 GB] inherit
  ACTIVE            '/dev/datavg/ftplv' [2.00 GB] inherit
  ACTIVE            '/dev/datavg/maclv' [30.00 GB] inherit
  ACTIVE            '/dev/datavg/MacPool100Glv' [100.00 GB] inherit
  ACTIVE            '/dev/rootvg/homelv' [152.00 MB] inherit
  ACTIVE            '/dev/rootvg/slashlv' [952.00 MB] inherit
  ACTIVE            '/dev/rootvg/tmplv' [3.00 GB] inherit
  ACTIVE            '/dev/rootvg/usrlv' [6.66 GB] inherit
  ACTIVE            '/dev/rootvg/varlv' [4.00 GB] inherit
  ACTIVE            '/dev/rootvg/srclv' [4.46 GB] inherit
  ACTIVE            '/dev/rootvg/muninlv' [1.00 GB] inherit
  ACTIVE            '/dev/rootvg/swap0' [7.45 GB] inherit
  ACTIVE            '/dev/rootvg/fileslv' [6.00 GB] inherit

3. Fire up dd command to copy block by block the contents of the source lv:

core:~# time dd if=/dev/datavg/MacPool100Glv of=/dev/bkupvg/MacPool100Glv bs=4M
25600+0 records in
25600+0 records out
107374182400 bytes (107 GB) copied, 1768.24 s, 60.7 MB/s

real	29m28.256s
user	0m0.120s
sys	3m41.034s

Now you have both lv with exactly the same data.

Note: In this example, the source lv was not mounted/used. If yours is mounted and in use, you can create a snapshot:

/sbin/lvcreate -L10G -s -n snap100glv /dev/datavg/MacPool100Glv
time dd if=/dev/datavg/snap100glv of=/dev/bkupvg/MacPool100Glv bs=4M