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.

As Vineeth pointed above in his comment, 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 file name that holds the lambda handler.

lambda_handler => {your-python-script-file-name}.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.

There are likely two issues here:

1. Python packages which have C bindings need to be built (pip install) on a machine with the same architecture as that which Lambda functions run (i.e., Linux)
2. With AWS Lambda, you are responsible for managing Python's path so it can find your dependencies. You likely need to update the path at runtime.

To solve #1, I use the official Python Docker image.

docker run --rm -it \
        -v `pwd`:/code \
        python:2 bash

Now, whenever you do a pip install -t lib numpy or the like, you will get the correct .so files. The trick here is using the volume argument (-v) so that the when you shut the container down the lib directory is preserved on your host machine.

To solve 2, I always structure my serverless/lambda project like this:

$ tree -L 2
.
├── handler.py
├── lib
│   └── numpy
└── serverless.yml

That is, all of my dependencies go inside lib.

pip install -t lib numpy

At the top of handler.py, I always have these 4 lines:

import os
import sys

CWD = os.path.dirname(os.path.realpath(__file__))
sys.path.insert(0, os.path.join(CWD, "lib"))

# now it's ok to import extra libraries
import numpy as np

After the sys.path.insert, any imports for your packages will work.