Cannot use the same Lambda version for 2 CloudFront distributions

From #4237:

Reproduction Steps

import * as cdk from "@aws-cdk/core";
import * as s3 from "@aws-cdk/aws-s3";
import * as lambda from "@aws-cdk/aws-lambda";
import * as cloudfront from "@aws-cdk/aws-cloudfront";

class SharedPwaLambdasStack extends cdk.Stack {
  addCspHeadersFunction: lambda.Function;

  constructor(scope: cdk.Construct, name: string, props?: cdk.StackProps) {
    super(scope, name, props);

    this.addCspHeadersFunction = new lambda.Function(this, "AddCspHeaders", {
      runtime: lambda.Runtime.NODEJS_8_10,
      handler: "index.handler",
      code: lambda.Code.fromInline("irrelevant"),
    });
  }
}

interface PwaStackProps extends cdk.StackProps {
  addCspHeadersFunction: lambda.Function;
}

class PwaStack extends cdk.Stack {
  constructor(scope: cdk.Construct, name: string, props: PwaStackProps) {
    super(scope, name, props);

    const bucket = new s3.Bucket(this, `${name}Bucket`);

    const distribution = new cloudfront.CloudFrontWebDistribution(this, `${name}Distribution`, {
      originConfigs: [
        {
          s3OriginSource: {
            s3BucketSource: bucket,
          },
          behaviors: [
            {
              isDefaultBehavior: true,
              lambdaFunctionAssociations: [
                {
                  eventType: cloudfront.LambdaEdgeEventType.VIEWER_RESPONSE,
                  lambdaFunction: props.addCspHeadersFunction.latestVersion,
                },
              ],
            },
          ],
        },
      ],
    });
  }
}

const app = new cdk.App();

const sharedPwaLambdasStack = new SharedPwaLambdasStack(app, "SharedPwaLambdas");

const websitePwa = new PwaStack(app, "WebsitePwa", {
  addCspHeadersFunction: sharedPwaLambdasStack.addCspHeadersFunction,
});

// If you comment the following stack, it will work.
const adminPwa = new PwaStack(app, "AdminPwa", {
  addCspHeadersFunction: sharedPwaLambdasStack.addCspHeadersFunction,
});

Error Log

cdk synth
yarn run v1.19.0
$ /code/node_modules/.bin/ts-node index.ts

/code/node_modules/@aws-cdk/core/lib/construct.ts:512
      throw new Error(`There is already a Construct with name '${childName}' in ${typeName}${name.length > 0 ? ' [' + name + ']' : ''}`);
            ^
Error: There is already a Construct with name '$LATEST' in Function [AddCspHeaders]
    at ConstructNode.addChild (/code/node_modules/@aws-cdk/core/lib/construct.ts:512:13)
    at new ConstructNode (/code/node_modules/@aws-cdk/core/lib/construct.ts:144:18)
    at new Construct (/code/node_modules/@aws-cdk/core/lib/construct.ts:563:17)
    at new Resource (/code/node_modules/@aws-cdk/core/lib/resource.ts:61:5)
    at new FunctionBase (/code/node_modules/@aws-cdk/aws-lambda/lib/function-base.ts:139:1)
    at new LatestVersion (/code/node_modules/@aws-cdk/aws-lambda/lib/function-base.ts:336:5)
    at Function.get latestVersion [as latestVersion] (/code/node_modules/@aws-cdk/aws-lambda/lib/function-base.ts:233:12)
    at new PwaStack (/code/cloud/index.ts:42:63)
    at Object.<anonymous> (/code/cloud/index.ts:62:18)
    at Module._compile (internal/modules/cjs/loader.js:936:30)
error Command failed with exit code 1.
info Visit https://yarnpkg.com/en/docs/cli/run for documentation about this command.

Environment

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Other

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This is 🐛 Bug Report

[iliapolo]

I believe the problem is with the dual reference to props.addCspHeadersFunction.latestVersion, which creates multiple instances, with the same scope and id:

https://github.com/aws/aws-cdk/blob/9ff55aeeed49d89bf13b2baf9025a1f4e038aa43/packages/%40aws-cdk/aws-lambda/lib/function-base.ts#L246-L248

A workaround could be storing the latest version in a const, and passing an IVersion, instead of a Function:

const sharedPwaLambdasStack = new SharedPwaLambdasStack(app, "SharedPwaLambdas");

const latestVersion = sharedPwaLambdasStack.addCspHeadersFunction.latestVersion;

const websitePwa = new PwaStack(app, "WebsitePwa", {
  addCspHeadersFunctionVersion: latestVersion,
});

// If you comment the following stack, it will work.
const adminPwa = new PwaStack(app, "AdminPwa", {
  addCspHeadersFunctionVersion: latestVersion,
});

[skinny85]

cc @skyrpex