CODE EXAMPLE FOR TYPESCRIPT

invoke lambda after cdk deploy

// Using Custom resources
const checkExecutionLambda = new lambda.Function(this, 'CheckExecutionFunction', {
    runtime: lambda.Runtime.NODEJS_12_X,
    handler: 'step-func.handler',
    code: lambda.Code.fromAsset(path.join(__dirname, '../lambda')),
    memorySize: 256,
    timeout: cdk.Duration.minutes(15),
    // tracing: lambda.Tracing.ACTIVE,
    environment: {
        STATE_MACHINE_ARN: ecrStateMachine.stateMachineArn
    }
});    

//Run checkExecutionLambda on Create
const lambdaTrigger = new cr.AwsCustomResource(this, 'StatefunctionTrigger', {
    policy: cr.AwsCustomResourcePolicy.fromStatements([new iam.PolicyStatement({
        actions: ['lambda:InvokeFunction'],
        effect: iam.Effect.ALLOW,
        resources: [checkExecutionLambda.functionArn]
    })]),
    timeout: cdk.Duration.minutes(15),
    onCreate: {
        service: 'Lambda',
        action: 'invoke',
        parameters: {
            FunctionName: checkExecutionLambda.functionName,
            InvocationType: 'Event'
        },
        physicalResourceId: cr.PhysicalResourceId.of('JobSenderTriggerPhysicalId')
    },
    onUpdate: {
        service: 'Lambda',
        action: 'invoke',
        parameters: {
            FunctionName: checkExecutionLambda.functionName,
            InvocationType: 'Event'
        },
        physicalResourceId: cr.PhysicalResourceId.of('JobSenderTriggerPhysicalId')
    }
})