Based on the documentation it looks like you are invoking the lambda correctly. It is how I do it as well. When setting the FunctionName parameter make sure it matches exactly to the name of the lambda as deployed in AWS not as named in the serverless template.
In this case I would look closer at the logs for the calling lambda to be sure it is failing where you think it is failing. The 500 HTTP response just indicates the lambda failed. It could be on any part of the code. So review the lambda logs for detail on where it might be failing.