I have fixed this issue, here is my description of how it happened and how I fixed it:
I set this up using the instructions on the website, on a Pi 3B. I followed the setup wizard and selected my screen - a 4" Waveshare LCD Screen. I selected LCD4-Show; this is the driver the LCD screens manual suggested. It didn't seem to do anything.
I then followed the instructions for manual driver install, and found the driver and installed it via SSH. The screen now works.
However, during bootup I now get the message “/etc/rc.local: fbcp: not found”.
Some googling took me to this page: https://github.com/waveshare/LCD-show/issues/8
SSH'ing into the DUT and sending the following commands (some of them require SUDO) fixed the issue:
apt-get --yes --force-yes install cmake
cd /tmp
curl -LO https://github.com/tasanakorn/rpi-fbcp/archive/master.zip
unzip master.zip
cd rpi-fbcp-master
mkdir build
cd build
cmake ..
make
install fbcp /usr/local/bin/fbcp
cd ../..
rm -rf rpi-fbcp-master
