Final answer:
To ensure an AWS Lambda function can be called via an HTTP POST request, setting up an API Gateway is the most operationally efficient solution. It securely exposes the Lambda function to the web and manages traffic, authorization, and other functionalities.
Step-by-step explanation:
The most operationally efficient solution to ensure that a third-party analytics service can call an AWS Lambda function using an HTTP POST request, is by setting up an API Gateway. API Gateway acts as a front door for an AWS Lambda function, allowing it to receive HTTP requests securely. You would configure API Gateway to trigger the Lambda function when it receives the correct POST request. To maintain the system's security, it is crucial to implement proper authentication and authorization mechanisms, such as API keys or IAM roles. Additionally, API Gateway can handle traffic management, CORS support, request and response transformations, and more, which adds to the operational efficiency and security of the webhook setup.