AWS Lambda Functions Unable to import module 'lambda_function': No module named 'lambda_function' error

Question

On AWS I am creating a Lambda Function like this:

from __future__ import print_function
import time
import uuid
import sys
import socket
import elasticache_auto_discovery
from pymemcache.client.hash import HashClient

# ElastiCache settings
elasticache_config_endpoint = "my-endpoint"
nodes = elasticache_auto_discovery.discover(elasticache_config_endpoint)
nodes = map(lambda x: (x[1], int(x[2])), nodes)
memcache_client = HashClient(nodes)

######
# This function puts into memcache and get from it.
# Memcached is hosted using elasticache
######
def handler(event, context):

    # Create a random UUID... this will be the sample element we add to the cache.
    uuid_in = uuid.uuid4().hex
    
    # Put the UUID to the cache.
    memcache_client.set('uuid', uuid_in)
    
    # Get the item (UUID) from the cache.
    uuid_out = memcache_client.get('uuid')
    
    # Print the results
    if uuid_out == uuid_in:
        # this print should see the CloudWatch Logs and Lambda console.
        print "Success: Inserted: %s. Fetched %s from memcache." %(uuid_in, uuid_out)
    else:
        raise Exception("Bad value retrieved :(. Expected %s got %s." %(uuid_in, uuid_out)) 

    return "Fetched value from Memcached"

I get this error, on the execution:

{
  "errorMessage": "Unable to import module 'lambda_function': No module named 'lambda_function'",
  "errorType": "Runtime.ImportModuleError",
  "stackTrace": []
}

I have followed this tutorial: https://docs.aws.amazon.com/AmazonElastiCache/latest/mem-ug/Lambda.html

Any suggestion about the problem source?