[Ethereum] Can’t connect to EC2 Ethereum node from AWS Lambda

I tried to continue the discussion on this similar question: Connection Error – Couldn't connect to ethereum node on AWS at http://xx.xxx.xx.xxx:8545. Mods told me to create a new one so here goes.

I have an EC2 instance running an Ethereum node (Parity in my case). The instance is public to the world. I can run some simple code on my local machine at home and connect to the AWS instance:

const Web3 = require('web3')
let web3 = new Web3(
  new Web3.providers.HttpProvider('http://<EC2_PUBLIC_IP>:8545')
)
console.log(web3.eth.blockNumber)

This works fine from any computer that can connect to the internet.

I want to set up a Lambda function that can set up a web3 connection to this node. I've tried a simple function like this:

const Web3 = require('web3')

module.exports.hello = (event, context, callback) => {
  let web3 = new Web3(
    new Web3.providers.HttpProvider(
      'http://<EC2_PUBLIC_IP>:8545'
    )
  )
  callback(
    null,
    success({
      blockNumber: web3.eth.blockNumber
    })
  )
}

When I run this, I always get the error:

Error: CONNECTION ERROR: Couldn't connect to node http://<EC2_PUBLIC_IP>:8545.

I have tried everything and verified that the Lambda can talk to the EC2 by serving an HTTP request (they are in the same VPC). I tried to use the private IP instead of public, DNS instead of IP address, everything.

I've read that people have been able to have Lambda functions call contracts, so I think this has to be possible.

Any ideas on what we can try?