diff --git a/packages/@aws-cdk/aws-lambda-python/README.md b/packages/@aws-cdk/aws-lambda-python/README.md
index 2a8de2d34c4de..af19fd7ca037f 100644
--- a/packages/@aws-cdk/aws-lambda-python/README.md
+++ b/packages/@aws-cdk/aws-lambda-python/README.md
@@ -163,6 +163,31 @@ const codeArtifactAuthToken = execSync(`aws codeartifact get-authorization-token
 
 const indexUrl = `https://aws:${codeArtifactAuthToken}@${domain}-${domainOwner}.d.codeartifact.${region}.amazonaws.com/pypi/${repoName}/simple/`;
 
+new lambda.PythonFunction(this, 'function', {
+  entry,
+  runtime: Runtime.PYTHON_3_8,
+  bundling: {
+    environment: { PIP_INDEX_URL: indexUrl },
+  },
+});
+```
+
+If you also want to use the Code Artifact repo for initializing the Docker image for bundling, use `buildArgs`:
+
+```ts
+import { execSync } from 'child_process';
+
+const entry = '/path/to/function';
+const image = DockerImage.fromBuild(entry);
+
+const domain = 'my-domain';
+const domainOwner = '111122223333';
+const repoName = 'my_repo';
+const region = 'us-east-1';
+const codeArtifactAuthToken = execSync(`aws codeartifact get-authorization-token --domain ${domain} --domain-owner ${domainOwner} --query authorizationToken --output text`).toString().trim();
+
+const indexUrl = `https://aws:${codeArtifactAuthToken}@${domain}-${domainOwner}.d.codeartifact.${region}.amazonaws.com/pypi/${repoName}/simple/`;
+
 new lambda.PythonFunction(this, 'function', {
   entry,
   runtime: Runtime.PYTHON_3_8,
@@ -172,4 +197,33 @@ new lambda.PythonFunction(this, 'function', {
 });
 ```
 
-This type of an example should work for `pip` and `poetry` based dependencies, but will not work for `pipenv`.
+**Note:** Setting custom build args for bundling will force the base bundling image to be rebuilt every time (i.e. skip the Docker cache).
+
+Setting only environment variable should work for `pip` and `poetry` based dependencies, whereas `pipenv` based dependencies will require **both** build args and environment variables to be set.
+
+
+Example for using Code Artifact with `pipenv`-based dependencies:
+
+```ts
+import { execSync } from 'child_process';
+
+const entry = '/path/to/function';
+const image = DockerImage.fromBuild(entry);
+
+const domain = 'my-domain';
+const domainOwner = '111122223333';
+const repoName = 'my_repo';
+const region = 'us-east-1';
+const codeArtifactAuthToken = execSync(`aws codeartifact get-authorization-token --domain ${domain} --domain-owner ${domainOwner} --query authorizationToken --output text`).toString().trim();
+
+const indexUrl = `https://aws:${codeArtifactAuthToken}@${domain}-${domainOwner}.d.codeartifact.${region}.amazonaws.com/pypi/${repoName}/simple/`;
+
+new lambda.PythonFunction(this, 'function', {
+  entry,
+  runtime: Runtime.PYTHON_3_8,
+  bundling: {
+    buildArgs: { PIP_INDEX_URL: indexUrl },
+    environment: { PIP_INDEX_URL: indexUrl },
+  },
+});
+```