Problems w/ local repository in 16.04 with apt-mirror. How to update from client?

As mentioned in the comment of the question, this was solved by also adding the i386-packages to the local repository. Did the following, minor changes to /etc/apt/mirror.list: on the host-side (had to download approx 40GB extra in packages, if I remember correctly):

############# config ##################
#
set base_path /repo
#
# set mirror_path  $base_path/mirror
# set skel_path    $base_path/skel
# set var_path     $base_path/var
# set cleanscript $var_path/clean.sh
# set defaultarch  <running host architecture>
# set postmirror_script $var_path/postmirror.sh
# set run_postmirror 0
set nthreads     20
set _tilde 0
#
############# end config ##############

deb-amd64 http://archive.ubuntu.com/ubuntu xenial main restricted universe multiverse
deb-amd64 http://archive.ubuntu.com/ubuntu xenial-security main restricted universe multiverse
deb-amd64 http://archive.ubuntu.com/ubuntu xenial-updates main restricted universe multiverse

deb-i386 http://archive.ubuntu.com/ubuntu xenial main restricted universe multiverse
deb-i386 http://archive.ubuntu.com/ubuntu xenial-security main restricted universe multiverse
deb-i386 http://archive.ubuntu.com/ubuntu xenial-updates main restricted universe multiverse

clean http://archive.ubuntu.com/ubuntu

Can't explain why it works, but it does and it solved my problem. Stupid as it is.