The aws-cdk.aws-lambda-python L2 construct exist specifically for this.

Here's the documentation:

https://docs.aws.amazon.com/cdk/api/latest/docs/aws-lambda-python-readme.html

Typescript example form the docs above:

import * as lambda from "@aws-cdk/aws-lambda";
import { PythonFunction } from "@aws-cdk/aws-lambda-python";

new PythonFunction(this, 'MyFunction', {
  entry: '/path/to/my/function', // required
  index: 'my_index.py', // optional, defaults to 'index.py'
  handler: 'my_exported_func', // optional, defaults to 'handler'
  runtime: lambda.Runtime.PYTHON_3_6, // optional, defaults to lambda.Runtime.PYTHON_3_7
});

It will install dependencies from a poetry file, a pipfile, or requiremenets.txt

UPDATE:

It now appears as though there is a new type of (experimental) Lambda Function in the CDK known as the PythonFunction. The Python docs for it are here. And this includes support for adding a requirements.txt file which uses a docker container to add them to your function. See more details on that here. Specifically:

If requirements.txt or Pipfile exists at the entry path, the construct will handle installing all required modules in a Lambda compatible Docker container according to the runtime.

Original Answer:

So this is the awesome bit of code my manager wrote that we now use:

    def create_dependencies_layer(self, project_name, function_name: str) -> aws_lambda.LayerVersion:
        requirements_file = "lambda_dependencies/" + function_name + ".txt"
        output_dir = ".lambda_dependencies/" + function_name
        
        # Install requirements for layer in the output_dir
        if not os.environ.get("SKIP_PIP"):
            # Note: Pip will create the output dir if it does not exist
            subprocess.check_call(
                f"pip install -r {requirements_file} -t {output_dir}/python".split()
            )
        return aws_lambda.LayerVersion(
            self,
            project_name + "-" + function_name + "-dependencies",
            code=aws_lambda.Code.from_asset(output_dir)
        )

It's actually part of the Stack class as a method (not inside the init). The way we have it set up here is that we have a folder called lambda_dependencies which contains a text file for every lambda function we are deploying which just has a list of dependencies, like a requirements.txt.

And to utilise this code, we include in the lambda function definition like this:

        get_data_lambda = aws_lambda.Function(
            self,
            .....
            layers=[self.create_dependencies_layer(PROJECT_NAME, GET_DATA_LAMBDA_NAME)]
        )