Before you start - you need to create an IAM user that has limited permissions to Lambda only. You should follow these instructions remembering to substitute "Lambda" for "SES".
There are two ways to use AWS Lambda with Zapier:
Zapier provides data to your pre-built function.
This is the simplest but more strict option via the Invoke Function action - you tell us which function you want us to invoke and we'll provide the data to invoke it. You will write your code in the Amazon console or whatever medium you prefer.
Zapier provides data AND code to a special "sugar" function you add on our behalf.
This is a more flexible option that allows you to write code in your browser during Zap setup via the Run Code action - though you will need to upload a special "sugar" function that takes both data and the code you wrote during Zap setup. The special "sugar" function simply
evals the code as a convenience.