I have been trying to use pip install to install the cython and lxml packages under Python3.8 on Cygwin. However, this repeatedly fails with incomprehensible errors ranging from python errors to gcc header files not found, even though they are there. 
Because lxml depends on Cython, we need to make sure we have that working first. Unfortunately Cygwin's python3.8 doesn't yet support cython, it seems. So we are told to download and use the wheel from here.
pip install Cython-0.29.13-cp38-cp38-win32.whl
# This fails with:
#ERROR: Cython-0.29.13-cp38-cp38-win32.whl is not a supported wheel on this platform.
# Instead use:
pip install Cython --install-option="--no-cython-compile"
# OK!
Now let's try to install the lxml package.
pip install lxml
# FAIL
STATIC_DEPS=true pip3 install lxml
# FAIL
Let's check that Python.h exists: 
# find /usr/include -type f -name "Python.h"
/usr/include/python2.7/Python.h
/usr/include/python3.6m/Python.h
/usr/include/python3.8/Python.h
Ok...
So what is the problem?
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