Given AWS Lambda's strict timeouts, have you verified the same configuration & task will run to completion in a more typical environment first?
The error about the C-extension not being loaded doesn't require `cython` to be installed, but rather for full python/OS build tools to be available at the time gensim is installed. On Ubuntu, this usually means at least the `build-essentials' and 'python-dev' packages are installed before installing gensim. Essentially, watch the logs/errors very carefully when installing gensim & numpy/scipy, and address any problems indicated there before trying to use gensim.
- Gordon