support for stage variables in lambda and https integration

## :question: General Issue

### How to pass a stage variable to lambda function field in API Gateway?

I have an API Gateway that triggers a lambda function specified by a stage variable `stageVariables.lbfunc`.


How can I create this API Gateway with AWS CDK?

It looks like that I should create a special `handler` for [LambdaRestApi](https://docs.aws.amazon.com/cdk/api/latest/docs/@aws-cdk_aws-apigateway.LambdaRestApi.html).

But I can't find any example code for doing this.

The following is my current code. I wish that `LambdaIntegration`'s handler can be determined by a stage variable.

```
# dev_lambda_function should be replaced by something else
dev_lambda_function = lambda_.Function(self, "MyServiceHandler",
runtime=lambda_.Runtime.PYTHON_3_7,
code=lambda_.Code.asset("resources"),
handler="lambda_function.lambda_handler",
description="My dev lambda function"
)
stage_options = apigateway.StageOptions(stage_name="dev",
description="dev environment",
variables=dict(lbfunc="my-func-dev")
)
# What should I pass to the handler variable so that LambdaRestApi triggers the lambda function specified by the stage variable "stageVariables.lbfunc"?
api = apigateway.LambdaRestApi(self, "my-api",
rest_api_name="My Service",
description="My Service API Gateway",
handler=dev_lambda_function,
deploy_options=stage_options)
```

### Environment

- **CDK CLI Version:** 1.22.0 (build 309ac1b)
- **Module Version:**
- **OS:** OSX Mojave
- **Language:** Python

### Other information

Start by reading the LambdaRestApi and LambdaIntegration API documentation and the existing comment discussion. Determine whether the integration can select a Lambda target from the stageVariables.lbfunc value; done means an AWS CDK API can express this configuration and deploy an API Gateway stage that invokes the selected function.

Written by the indexing model from the issue text.