Lambda is the optimal solution for executing code in response to incoming web requests without the need for server management, and it is well-suited to handle unpredictable demand due to its ability to scale automatically with each trigger. This makes it ideal for situations where there are unexpected spikes in traffic. The pricing model based on the number of requests and the duration of execution also aligns with the variable workload, offering cost efficiency during periods of varying traffic intensity.

Other options like EC2 and ECS with Fargate involve server management at some level, and although Fargate abstracts the server management, it still requires configuration for container execution. SNS is primarily a messaging and notification service and does not directly handle execution of code in response to HTTP requests.