You actually do not require to scale lambda function, AWS Lambda scales them automatically on your behalf. Every time an event notification is received for your function, AWS Lambda quickly locates free capacity within its compute fleet and runs your code. Since your code is stateless, AWS Lambda can start as many copies of your function as needed without lengthy deployment and configuration delays. There are no fundamental limits to scaling a function. AWS Lambda will dynamically allocate capacity to match the rate of incoming events.
Hope this helps.