Using 2 puppetforge modules it is possible to configure LVM and docker engine.

https://forge.puppet.com/puppetlabs/lvm https://forge.puppet.com/puppetlabs/docker

I was unable to find any documentation on configuring direct-lvm though, but in the end it's not as complicated as I thought:

class { 'lvm':
  volume_groups => {
    'docker' => {
      physical_volumes => [ '/dev/sdb', ],
      logical_volumes  => {
        'thinpool' => {'extents' => '95%VG', 'thinpool' => true, 'createfs' => false},
      },
    },
  },
} ->

class { 'docker':
  version        => 'latest',
  manage_kernel  => false,
  storage_driver => 'devicemapper',
  dm_thinpooldev => '/dev/mapper/docker-thinpool',
}

# docker info
...
Storage Driver: devicemapper
 Pool Name: docker-thinpool
 Pool Blocksize: 262.1kB
 Base Device Size: 10.74GB
 Backing Filesystem: xfs
 Data file: 
 Metadata file: