Reinstall to existing encrypted partitions

The issue is that /etc/crypttab is not set up properly in the new system. You can fix this by booting into a live environment and then mounting your new system to fix it. The following is an overview of what you need to do, but device names will likely need to be changed for your system.

$ sudo -i
# cryptsetup open /dev/sda5 sda5_crypt # For root partition
# cryptsetup open /dev/sda6 sda6_crypt # For home partition
# lvchange -ay  # activates the logical volumes if you use llvm
# mkdir /mnt/ubuntu
# mount /dev/mapper/sda5_crypt /mnt/ubuntu
# mount /dev/mapper/sda6_crypt /mnt/ubuntu/home
# mount /dev/sda1 /mnt/ubuntu/boot
# mount --bind /dev /mnt/ubuntu/dev
# mount --bind /sys /mnt/ubuntu/sys
# mount -t proc none /mnt/ubuntu/proc

Now that the system is mounted you can add /mnt/ubuntu/etc/crypttab. It should look somewhat like this:

sda5_crypt UUID=12345678-9abc-def012345-6789abcdef01 none luks
sda6_crypt UUID=87654321-cba9-543210fed-01fedcba9876 none luks

You can find the UUID with ls -l /dev/disk/by-uuid. Note that the UUIDs used should be of the encrypted partitions, not the decrypted partitions.

You should also have a look at /mnt/ubuntu/etc/fstab and make sure the decrypted partitions are referenced by the sdaX_crypt names you assign in /mnt/ubuntu/etc/crypttab. If you decrypted the devices in the OS installer before installing, they might be referenced by some other names than what you assign yourself (e.g. luks-<uuid>). If you fail to do this, you might get an error saying cryptsetup: lvm is not available during boot.

Finally you can chroot into the new system to update the initramfs.

# chroot /mnt/ubuntu /bin/bash
# update-initramfs -u

And then you're ready to reboot into your new system.