I have a tried to setup Shapely on AWS Lambda but was getting the below error always.
module initialization error: Could not find lib geos_c or load
I hit this same issue, and was able to set up to build a layer for use in Lambda. I wrote it up as an open source package here https://github.com/bearflagrobotics/libgeos-lambda-build using Docker to build the binary distribution. You can just drop that in as a layer for your lambda function and run any version of Shapely or Python you want!