I have tested on amd64 with livecd-rootfs 2.408.41 from -proposed following the test case in the description.  My testing diverged from the test plan in that I am driving livecd-rootfs with ubuntu-old-fashioned[1] which builds with launchpad-buildd tools in a lxd container to replicate the buildd environment.  In this environment the build fails due to the lack of 'sudo':

[2018-12-10 18:06:08] lb_build 
P: Executing auto/build script.
Fetching core
Fetching pc-kernel
Fetching pc
Warning: for backwards compatibility, `ubuntu-image` falls back to `ubuntu-image snap` if no subcommand is given
-o/--output is deprecated; use -O/--output-dir instead
Crash in state machine
Traceback (most recent call last):
  File "/usr/lib/python3/dist-packages/ubuntu_image/__main__.py", line 341, in main
    list(state_machine)
  File "/usr/lib/python3/dist-packages/ubuntu_image/state.py", line 82, in __next__
    step()
  File "/usr/lib/python3/dist-packages/ubuntu_image/common_builder.py", line 337, in populate_filesystems
    self._populate_one_volume(name, volume)
  File "/usr/lib/python3/dist-packages/ubuntu_image/common_builder.py", line 290, in _populate_one_volume
    preserve_ownership=True)
  File "/usr/lib/python3/dist-packages/ubuntu_image/helpers.py", line 233, in mkfs_ext4
    with mount(img_file) as mountpoint:
  File "/usr/lib/python3.5/contextlib.py", line 59, in __enter__
    return next(self.gen)
  File "/usr/lib/python3/dist-packages/ubuntu_image/helpers.py", line 207, in mount
    run('sudo mount -oloop {} {}'.format(img, mountpoint))
  File "/usr/lib/python3/dist-packages/ubuntu_image/helpers.py", line 115, in run
    **args)
  File "/usr/lib/python3.5/subprocess.py", line 693, in run
    with Popen(*popenargs, **kwargs) as process:
  File "/usr/lib/python3.5/subprocess.py", line 947, in __init__
    restore_signals, start_new_session)
  File "/usr/lib/python3.5/subprocess.py", line 1551, in _execute_child
    raise child_exception_type(errno_num, err_msg)
FileNotFoundError: [Errno 2] No such file or directory: 'sudo'
Build failed
Traceback (most recent call last):
  File "/usr/lib/python2.7/dist-packages/lpbuildd/target/build_livefs.py", line 161, in run
    self.build()
  File "/usr/lib/python2.7/dist-packages/lpbuildd/target/build_livefs.py", line 152, in build
    self.run_build_command(["lb", "build"], env=base_lb_env)
  File "/usr/lib/python2.7/dist-packages/lpbuildd/target/build_livefs.py", line 79, in run_build_command
    return self.backend.run(args, cwd="/build", **kwargs)
  File "/usr/lib/python2.7/dist-packages/lpbuildd/target/lxd.py", line 490, in run
    subprocess.check_call(cmd, **kwargs)
  File "/usr/lib/python2.7/subprocess.py", line 541, in check_call
    raise CalledProcessError(retcode, cmd)
CalledProcessError: Command '['lxc', 'exec', 'lp-xenial-amd64', '--env', 'PROJECT=ubuntu-core', '--env', 'ARCH=amd64', '--', '/bin/sh', '-c', 'cd /build && linux64 lb build']' returned non-zero exit status 1

The rootfs used by the builders does not have 'sudo' installed, it should be a package dependency  for livecd-rootfs based on this testing.  I'm going to mark this as verification-failed-xenial.  However, I did install 'sudo' manually in the build environment and this resulted in a successful build with output in /build of livecd.ubuntu-core.img.xz, livecd.ubuntu-core.manifest, livecd.ubuntu-core.model-assertion, and snaps.manifest.

[1] https://github.com/chrisglass/ubuntu-old-fashioned/blob/master/old-fashioned-image-build