I created my Alexa Skill as an AWS Lambda Node.js app based on one of the provided examples in the Alexa Skills Kit. I followed all the instructions:
I noticed you didn't mention setting your Event Source. Here's the snippet from the documentation here.
Add the Alexa Skills Kit Event Source
Adding the Alexa Skills Kit event source to your function grants Alexa the necessary invocation permissions for your function.
Log in to the AWS Management Console and navigate to AWS Lambda.
Select your function in the list.
Click Actions and then select Add event source.
Select Alexa Skills Kit from the Event source type.
Click Submit.
Additionally, feel free to check out the Alexa Skills Kit Knowledge Base sub-forum for a list of common Q&A here.
Thanks!