Comment 13 for bug 1657646

TL;DR "sudo apt install thin-provisioning-tools" fixes it.

Adding debugging steps here for posterity.

ubuntu@15-89:~$ cat /etc/docker/daemon.json
{
  "storage-driver": "devicemapper",
  "storage-opts": [
    "dm.thinpooldev=/dev/mapper/docker--storage-thinpool",
    "dm.use_deferred_removal=true",
    "dm.use_deferred_deletion=true"
  ]
}

After reboot:

ubuntu@15-89:~$ docker info
Cannot connect to the Docker daemon. Is the docker daemon running on this host?

/var/log/syslog:
Jun 20 20:42:11 15-89 dockerd[1542]: time="2017-06-20T20:42:11.938899425Z" level=fatal msg="Error starting daemon: error initializing graphdriver: devicemapper: Non existing device docker--storage-thinpool"

root@15-89:~# ll /dev/mapper/
total 0
drwxr-xr-x 2 root root 60 Jun 20 20:41 ./
drwxr-xr-x 19 root root 3760 Jun 20 20:41 ../
crw------- 1 root root 10, 236 Jun 20 20:41 control

But lvs shows it:
root@15-89:~# lvs
  LV VG Attr LSize Pool Origin Data% Meta% Move Log Cpy%Sync Convert
  thinpool docker-storage twi---t--- 38.00g

vgchange -a y didn't work, complaining that a tool called thin_check wasn't available. This tool comes with thin-provisioning-tools.

I then installed thin-provisioning-tools and rebooted one more time. Now docker runs fine.

What's left to check here is if perhaps thin-provisioning-tools should be a strong or weak dependency of docker.io, like a Recommends or Suggests.