As it is described in the Amazon official documentation link here It is as simple as just creating a zip of all the folder contents after installing the required packages in your folder where you have your python lambda code.
The very first step in moving from an inline code editor to a zip file upload approach is to change your lambda function handler name under configuration settings to include the python script filename that holds the lambda handler.
Other solutions like python-lambda and lambda-uploader help with simplifying the process of uploading and the most importantly LOCAL TESTING. These will save a lot of time in development.
Hope this helps!!
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