2011-01-10.

Already familiar with resizing RAID devices (e.g. after adding 
a disk and growing the array) online, then resizing ext3 filesystem
online to fill the new device.

Now want to do it with luks-based encryption within linux LVM.
Thanks to Google and 
http://www.debian-administration.org/article/536/Resizing_Encrypted_Filesystems
for preventing any thought or manual-reading from being needed.

# opening the encrypted device
cryptsetup luksOpen /dev/DEVICE NAME
ls -l /dev/mapper/NAME

######
# /the/ needed command to resize the encrypted device
cryptsetup resize NAME
######

# then of course, to make the filesystem bigger to fill the new space:
resize2fs /dev/mapper/NAME


All working well; works even online.