You'll want to create the new lvol and filesystem in your new VG, then backup/restore the data. As you can see, this will require an outage so you could at least unmount the old filesystem to mount the new one under the same mount point--don't forget to update /etc/fstab.
Before creating your new lvol and fs, use lvdisplay and 'fstyp -v' to view details about them both. If the source and destination lvol are identical sizes, you would be able to use dd to 'clone' the unmounted filesystem (ex/ if=src_lvol of=dest_lvol)... otherwise, backup and restore. After you are satisfied that all is well, you could remove the old lvol.
Hope this helps,
-denver
