How to install dependencies of lambda functions upon cdk build with AWS CDK

This functionality really is missing. You'll need to write your own packaging. Keep in mind that lambda dependencies must be built on a system with the same architecture as the target system in AWS (Linux) if any of the dependencies (such as Numpy) uses a shared library with native C code.

There's a Docker image available which aims to provide an environment as close to AWS as possible: lambci/lambda:build-python3.7

So if you're building on any non-Linux architecture, you might need this for some more complex lambda functions.

EDIT: I opensourced my Python code for lambda packaging: https://gitlab.com/josef.stach/aws-cdk-lambda-asset

You can do this pretty easily with a local build script like this:

    const websiteRedirectFunction = new lambda.Function(
      this,
      "RedirectFunction",
      {
        code: lambda.Code.fromAsset(path.resolve(__dirname, "../../redirect"), {
          bundling: {
            command: [
              "bash",
              "-c",
              "npm install && npm run build && cp -rT /asset-input/dist/ /asset-output/",
            ],
            image: lambda.Runtime.NODEJS_12_X.bundlingDockerImage,
            user: "root",
          },
        }),
        handler: "index.redirect",
        tracing: lambda.Tracing.ACTIVE,
        runtime: lambda.Runtime.NODEJS_12_X,
      }
    );

Assuming you have a folder that you want to build and upload the handler and node_modules for Lambda.

From the docs:

When using lambda.Code.fromAsset(path) it is possible to bundle the code by running a command in a Docker container. The asset path will be mounted at /asset-input. The Docker container is responsible for putting content at /asset-output. The content at /asset-output will be zipped and used as Lambda code.