I’ve run into this problem as well intermittently. It always fixes itself after a bit. It’s likely a connectivity issue either between your server and Ubuntu packages, or simply with Ubuntu packages.
I ssh’d into the server and ran apt-update manually, the php7 ppa seems to be the culprit:
W: Failed to fetch http://ppa.launchpad.net/ondrej/php-7.0/ubuntu/dists/trusty/main/binary-amd64/Packages 404 Not Found
W: Failed to fetch http://ppa.launchpad.net/ondrej/php-7.0/ubuntu/dists/trusty/main/binary-i386/Packages 404 Not Found
It is a connection issue, but it won’t fix itself. The PPA changed early last month (Feb 5th), so you will need to update it. There have also been a few changes to the PHP role (updated modules, fixes for xdebug) which are worth incorporating too.
Do I have to manually change the PPA on the server (if so, could you give a pointer how that’s done?), or should that change automatically when reprovisioning after Trellis is updated? The thing is I’ve just updated Trellis, but still receive the PPA error message.