Warning, wall of text incoming. It's as well formatted as I could make it.
If we're going to answer this, we're going to answer the whole thing. I'm not doing another answer on this, so here goes:
Let's pretend you know absolutely nothing, and I'm feeding you keystrokes.
This tells you everything you need to know to do this WHOLE thing, with a little bit of this and this thrown in. Really, read.
You could have, by reading that, arrived at:
Boot Ubuntu 11.10 as live.
Open a terminal. The sizes I'm using are on a 40G virtual disk. We're doing this all as root
sudo su
apt-get install lvm2
fdisk /dev/sda
n
p
1
[enter]
+1000M
t
83
n
[enter]
[enter]
t
2
8e
w
Which means, open dev/sda, new primary partition in position 1 of size no less than 1000MB with type ext3 or better, new primary partition in position 2 of type LVM, and write to disk.
Because I spelled it out, I'm going to assume you're running that setup EXACTLY.
We'll use /dev/sda1 for /boot and /dev/sda2 for EVERYTHING ELSE. You can change the sizes to suit your bare metal install, but this was for a VM to answer your question.
pvcreate /dev/sda2
vgcreate iammaster /dev/sda2
lvcreate --name lvubuntu --size 10G iammaster
lvcreate --name lvhome --size 12G iammaster
lvcreate --name lvyouarestudent --size 13G iammaster
lvcreate --name lvswap --size 4G iammaster
That says create a physical volume on /dev/sda2, a volume group of name iammaster on /dev/sda2, and logical volumes lvubuntu, lvhome, lvyouarestudent, and lvswap on volume group iammaster.
lvdisplay iammaster
Just to check. Then format...
cryptsetup -c aes-cbc-essiv:sha256 -y -s 256 luksFormat /dev/mapper/iammaster-lvyouarestudent
YES
*passphrase twice*
cryptsetup -c aes-cbc-essiv:sha256 -y -s 256 luksFormat /dev/mapper/iammaster-lvhome
YES
*passphrase twice*
cryptsetup -c aes-cbc-essiv:sha256 -y -s 256 luksFormat /dev/mapper/iammaster-lvswap
YES
*passphrase twice*
cryptsetup -c aes-cbc-essiv:sha256 -y -s 256 luksFormat /dev/mapper/iammaster-lvubuntu
YES
*passphrase twice*
Okie-doke. Now you've got encrypted LVM. Mount your crypt partitions.
cryptsetup luksOpen /dev/mapper/iammaster-lvswap swap
*enter passphrase*
cryptsetup luksOpen /dev/mapper/iammaster-lvubuntu ubuntu
*enter passphrase*
cryptsetup luksOpen /dev/mapper/iammaster-lvhome home
*enter passphrase*
And the formatting and enabling swap...
mkswap /dev/mapper/swap
swapoff -a
swapon /dev/mapper/swap
mkfs.ext4 /dev/mapper/ubuntu
mkfs.ext4 /dev/mapper/home
Install per normal (custom) and don't reboot. Note that you have to do a non-standard install and double click to on the logical volumes to choose FS-Type and mount-point. Don't forget /dev/sda1 as boot. We then click install now. After a couple of continues, you're on your way. Click continue testing NOT restart now.

Get directories ready
mkdir /mnt/ubuntu
mount /dev/mapper/ubuntu /mnt/ubuntu
Mount the special filesystems and boot
mount --bind /dev /mnt/ubuntu/dev
mount --bind /proc /mnt/ubuntu/proc
mount --bind /sys /mnt/ubuntu/sys
mount /dev/sda1 /mnt/ubuntu/boot
And chroot/install lvm/crypt
chroot /mnt/ubuntu
apt-get install cryptsetup lvm2 dmsetup
Next we need crypttab so we only unlock our disks once
ubuntu /dev/mapper/iammaster-lvubuntu none luks
home /dev/mapper/iammaster-lvhome /etc/home.key luks
swap /dev/mapper/iammaster-lvswap /dev/urandom swap,cipher=aes-cbc-essiv:sha256
cat /etc/crypttab
cat /etc/fstab
*make sure everything matches*
dd if=/dev/urandom of=/etc/home.key bs=256 count=1
cryptsetup luksAddKey /dev/mapper/iammaster-lvhome /etc/home.key
*enter passphrase*
Now for initramfs
*edit /etc/initramfs-tools/modules*
aes-i586
dm-crypt
dm-mod
sha256
update-initramfs -k all -c
update-grub2
grub-install /dev/sda
init 6
Now on to repeating all this for backtrack...because if you do it manually right once, the next time should be the same
startx
*open terminal*
vgchange -a y
cryptsetup -c aes-cbc-essiv:sha256 -y -s 256 luksFormat /dev/mapper/iammaster-lvswap
YES
*passphrase twice*
cryptsetup luksOpen /dev/mapper/iammaster-lvswap swap
*enter passphrase*
mkswap /dev/mapper/swap
swapoff -a
swapon /dev/mapper/swap
cryptsetup luksOpen /dev/mapper/iammaster-lvubuntu ubuntu
*enter passphrase*
cryptsetup luksOpen /dev/mapper/iammaster-lvhome home
*enter passphrase*
cryptsetup luksOpen /dev/mapper/iammaster-lvyouarestudent bt
*enter passphrase*
mkfs.ext4 /dev/mapper/bt
Install specify manual, specify mountpoints(shared /boot too. if you're using one behind/stable Ubuntu and edge BT it shouldn't be a problem with clobbering...if you're still concerned, add another boot partition), don't format. At step 8, advanced

When it finishes continue testing again, just like last time:
Get directories ready
mkdir /mnt/bt
mount /dev/mapper/bt /mnt/bt
mkdir /mnt/tempmount
mount /dev/mapper/ubuntu /mnt/tempmount
cp /mnt/tempmount/etc/home.key /mnt/bt/etc/home.key
Mount the special filesystems and boot
mount --bind /dev /mnt/bt/dev
mount --bind /proc /mnt/bt/proc
mount --bind /sys /mnt/bt/sys
mount /dev/sda1 /mnt/bt/boot
And chroot/install lvm/crypt
chroot /mnt/bt
apt-get install cryptsetup lvm2 dmsetup
Next we need crypttab so we only unlock our disks once
bt /dev/mapper/iammaster-lvyouarestudent none luks
home /dev/mapper/iammaster-lvhome /etc/home.key luks
swap /dev/mapper/iammaster-lvswap /dev/urandom swap,cipher=aes-cbc-essiv:sha256
cat /etc/crypttab
cat /etc/fstab
*make sure everything matches*
Now for initramfs
*edit /etc/initramfs-tools/modules*
aes-i586
dm-crypt
dm-mod
sha256
update-initramfs -k all -c
init 6
Reboot to ubuntu live media
sudo su
apt-get install lvm2
vgchange -a y
cryptsetup luksOpen /dev/mapper/iammaster-lvubuntu ubuntu
*passphrase*
mkdir /mnt/ubuntu
mount /dev/mapper/ubuntu /mnt/ubuntu
*insert the bind steps and mount boot steps from before again*
chroot /mnt/ubuntu
update-initramfs -k all -c
update-grub2
grub-install /dev/sda
init 6
Just change /dev/mapper/ubuntu to /dev/mapper/bt and pass the right kernel arguments and you're done.
I went to a lot of trouble to create this tutorial. I hope you appreciate it.
*you may have to do this every time BT gets a kernel update*