I now have GCC working on AWS Lambda.
Thanks to Abhishek Patnia I was able to get most of the way there.
A few tweaks were required.
Refer to the current lambda docs for the latest recommended AMI which is currently amzn-ami-hvm-2017.03.1.20170812-x86_64-gp2.
The most vexing hangup was gathering additional static libraries from /usr/lib64/.
One helpful trick was piping stdio/stderr out to a file as the Python AWS Lambda handler wrapper was really not happy about nonzero return values.
gcc -v hello.c 2> any_errors