You can't just put your API in Lambda and expect to to scale infinitely. Serverless runs on servers, so it very much depends what that API actually does. For ex

You can't just put your API in Lambda and expect to to scale infinitely. Serverless runs on servers, so it very much depends what that API actually does. For example, if your API runs a query on your database, the limit to how it scales will depend on how quickly your database instance can run that query.