reinstalling LVM+LUKS on Ubuntu 14.10 -> http://joh.fi/ubuntu/encryption/lvm/cryptsetup/2014/03/18/ubuntu-13.10-encrypted-lvm-installation.html

00.reinstalling-LVM+LUKS-on-Ubuntu.md

• Install Ubuntu 13.10 on top of encrypted lvm by Janne Haapsaari
• HOWTO: install and reinstall on an encrypted LUKS/LVM system on UbuntuForums

Might help

• 14.04: Prepared Disk (LVM/LUKS/LVM), Installed. Reboots to BusyBox; Chroot Fix Fails.
• Full disk encryption with Ubuntu (9.04 Jaunty or newer), LVM and LUKS
• Full disk encryption with Ubuntu (9.04 Jaunty or newer), LVM and LUKS

Going further

• Ubuntu with Grub2 + LUKS encrypted LVM root + hidden USB keyfile

01.cryptsetup-luksOpen

sudo cryptsetup luksOpen /dev/sda5 luks_container

02a.lvdisplay.out

sudo lvdisplay 
  --- Logical volume ---
  LV Path                /dev/mint-vg/root
  LV Name                root
  VG Name                mint-vg
  LV UUID                ZXld2t-7wOU-Vw5p-4h4Q-w8is-yhCf-z7hLX2
  LV Write Access        read/write
  LV Creation host, time mint, 2014-05-22 00:01:06 +0000
  LV Status              available
  # open                 0
  LV Size                8.55 GiB
  Current LE             2188
  Segments               3
  Allocation             inherit
  Read ahead sectors     auto
  - currently set to     256
  Block device           252:1
   
  --- Logical volume ---
  LV Path                /dev/mint-vg/home
  LV Name                home
  VG Name                mint-vg
  LV UUID                89jWuf-uKik-4JDF-BJUp-GbyM-UPje-WyotAG
  LV Write Access        read/write
  LV Creation host, time mint, 2014-05-22 00:53:52 +0000
  LV Status              available
  # open                 0
  LV Size                2.00 GiB
  Current LE             512
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto
  - currently set to     256
  Block device           252:2
   
  --- Logical volume ---
  LV Path                /dev/mint-vg/data
  LV Name                data
  VG Name                mint-vg
  LV UUID                1P2oWP-WEmN-2tKD-wkfh-GAlC-iCWv-XPTL3b
  LV Write Access        read/write
  LV Creation host, time mint, 2014-05-22 00:55:13 +0000
  LV Status              available
  # open                 0
  LV Size                100.00 GiB
  Current LE             25600
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto
  - currently set to     256
  Block device           252:3
   
  --- Logical volume ---
  LV Path                /dev/mint-vg/swap
  LV Name                swap
  VG Name                mint-vg
  LV UUID                HfQVJv-giT3-81W1-JJdY-kM4l-19uI-DVAlIX
  LV Write Access        read/write
  LV Creation host, time mint, 2014-05-31 19:47:33 +0000
  LV Status              available
  # open                 0
  LV Size                1.00 GiB
  Current LE             256
  Segments               1
  Allocation             inherit
  Read ahead sectors     auto
  - currently set to     256
  Block device           252:4

02b.luks-device-uuid

sudo blkid /dev/sda5
# /dev/sda5: UUID="db83deac-8302-47f0-804b-fb2b95f2b8fc" TYPE="crypto_LUKS"

03.chroot

# http://www.webupd8.org/2014/01/how-to-fix-non-bootable-ubuntu-system.html
sudo mkdir /mnt/
sudo mount /dev/mint-vg/root /mnt

# # # following command is CRITICAL! Otherwise you won't edit the correct config file
sudo mount /dev/sda1 /mnt/boot
# ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

sudo mount /dev/mint-vg/home /mnt/home
for p in /sys /proc /run /dev /dev/pts; do sudo mount --bind "$p" "/mnt$p"; done
sudo cp /etc/resolv.conf /mnt/etc/
sudo chroot /mnt

04.crypttab

# create: nano /etc/crypttab
# <target name> <source device> <key file> <options>
luks_container UUID=db83deac-8302-47f0-804b-fb2b95f2b8fc none luks,retry=1,lvm=mint-vg

05.cryptroot

# create: nano /etc/initramfs-tools/conf.d/cryptroot 
#CRYPTROOT=target=luks_container,source=/dev/disk/by-uuid/db83deac-8302-47f0-804b-fb2b95f2b8fc
CRYPTROOT=target=luks_container,source=/dev/disk/by-uuid/db83deac-8302-47f0-804b-fb2b95f2b8fc,lvm=mint-vg

06.initramfs-module

# see http://ubuntuforums.org/showthread.php?t=2222993
# in /etc/initramfs-tools/modules add f

06.update-initramfs

update-initramfs -k all -c

07a.grub

# set GRUB_CMDLINE_LINUX in : nano /etc/default/grub
GRUB_CMDLINE_LINUX="cryptopts=target=luks_container,source=/dev/disk/by-uuid/db83deac-8302-47f0-804b-fb2b95f2b8fc,lvm=mint-vg"
# or try (working on Linux Mint 17.2)
GRUB_CMDLINE_LINUX="cryptopts=target=luks_system,source=/dev/disk/by-uuid/db83deac-8302-47f0-804b-fb2b95f2b8fc,lvm=mint-vg"

07b.update-grub

update-grub
# if you got the following error, try:
# /usr/sbin/grub-mkconfig: 250: /usr/sbin/grub-mkconfig: cannot create /boot/grub/grub.cfg.new: Directory nonexistent
grub-install /dev/sda; update-grub

08.rewrite-grub-config

# If you got trouble with grub try re-creating the grub.cfg file, 
# see http://edoceo.com/notabene/grub-probe-error-cannot-find-device-for-root
sh -x /usr/sbin/grub-mkconfig -o /boot/grub/grub.cfg

I want mark ubuntu 15.10 doesn't support partitioned lvm with swap, because graphic installator crash. I recommend use ubuntu 14.04.3 ( http://releases.ubuntu.com/14.04.3/ ) and upgrade.

Thanks @ad-m, I edited following your comments.