The Debian-lxde LiveCD doesn't seem to include
cryptstup, which is needed to unlock the encrypted volume. I suggest you download
SystemRescueCD and use that to access your disk. Sample session with an encrypted Debian Wheezy install on /dev/sdb:
Code:
root@sysresccd /root % blkid
/dev/loop0: TYPE="squashfs"
/dev/loop1: UUID="df7879ce-c31c-418c-ade4-2b2a4135c735" TYPE="ext3"
/dev/sda1: LABEL="resccd-bs" UUID="a7765963-1e30-4e37-94cd-3f4c1edb836d" TYPE="ext3" PARTUUID="90b22297-01"
/dev/sdb1: UUID="2f6ad1e8-6683-40d7-bb47-70ad479a06a6" TYPE="ext2" PARTUUID="00028b2f-01"
/dev/sdb5: UUID="606de3d1-bb0d-4d63-999b-ecb8158a9662" TYPE="crypto_LUKS" PARTUUID="00028b2f-05"
/dev/sr0: UUID="2016-03-11-21-15-28-00" LABEL="sysresccd-4.5.2-mod" TYPE="iso9660"
root@sysresccd /root % cryptsetup luksOpen /dev/sdb5 myStuff
Enter passphrase for /dev/sdb5:
root@sysresccd /root % pvs
PV VG Fmt Attr PSize PFree
/dev/disk/by-id/dm-name-myStuff debian-7 lvm2 a-- 19.75g 0
root@sysresccd /root % lvs
LV VG Attr LSize Pool Origin Data% Meta% Move Log Cpy%Sync Convert
root debian-7 -wi-a----- 18.90g
swap_1 debian-7 -wi-a----- 872.00m
root@sysresccd /root % mkdir /mnt/tmp
root@sysresccd /root % mount -r /dev/debian-7/root /mnt/tmp
root@sysresccd /root % ls /mnt/tmp
bin etc lib media proc sbin sys var
boot home lib64 mnt root selinux tmp vmlinuz
dev initrd.img lost+found opt run srv usr
root@sysresccd /root %