Failed to sync output fields after first deploy

[titanjer]

I use this package for lambda@edge scenario. However, I get wrong CFN output fields (ap-northeast-1) after deployments for changed lambda code (us-east-1). Every time I modified lambda code in us-east-1 stack, the stack in ap-northeast-1 can not aware the changed.

You can see the two stack outputs below. NumLambdaEdgeStack.LambdaFuncArn (v4) and NumCloudfrontStack.OutputLambdaFuncArn (v2) should be the same.

Below is my code.

// lambda in us-east-1
export class NumLambdaEdgeStack extends Stack {

  constructor(scope: Construct, id: string, props: StackProps = {}) {
    super(scope, id, props);

    const managedPolicyArn = iam.ManagedPolicy.fromAwsManagedPolicyName('service-role/AWSLambdaBasicExecutionRole');

    const func = new PythonFunction(this, 'LambdaEdgeFunction', {
      entry: path.join(__dirname, './lambda/lambda-edge'),
      handler: 'handler',
      runtime: lambda.Runtime.PYTHON_3_8,
      role: new iam.Role(this, 'EdgeLambdaServiceRole', {
        assumedBy: new iam.CompositePrincipal(
          new iam.ServicePrincipal('lambda.amazonaws.com'),
          new iam.ServicePrincipal('edgelambda.amazonaws.com'),
        ),
        managedPolicies: [managedPolicyArn],
      }),
    });

    new CfnOutput(this, 'LambdaFuncArn', { value: func.currentVersion.functionArn });
  }
}

// cloudfront in ap-northeast-1
export interface NumCloudfrontStackProps extends StackProps {
  readonly lambdaStack: NumLambdaEdgeStack;
}

export class NumCloudfrontStack extends Stack {
  constructor(scope: Construct, id: string, props: NumCloudfrontStackProps) {
    super(scope, id, props);

    const outputs = new StackOutputs(this, 'LambdaFuncArn', {
      stack: props.lambdaStack,
    });
    const lambdaFuncArn = outputs.getAttString('LambdaFuncArn');

    origin = .....
    originRequestPolicy = .....

    const cf = new cloudfront.Distribution(this, 'Cloudfront', {
      defaultBehavior: {
        origin,
        originRequestPolicy,
        edgeLambdas: [
          {
            functionVersion: lambda.Version.fromVersionArn(this, 'EdgeLambdaFunctionArn', lambdaFuncArn),
            eventType: cloudfront.LambdaEdgeEventType.VIEWER_REQUEST,
          },
        ],
      },
      comment: 'num-cloudfront-test',
    });

    new CfnOutput(this, 'OutputLambdaFuncArn', { value: lambdaFuncArn });
  }
}