“ First, you don't need API Gateways if you use an AWS SDK. Like this guide shows. And of course you don't need a load balancer, because that's precisely one of the things that serverless takes care of for you :-)
More importantly, you didn't actually compare serverless to your current situation.
With serverless solutions you can typically save cost in terms of server management. Serverless isn't maintenance free, but you should be able to reduce your monthly cost (e.g. lower labor cost).
You're right to research whether it actually works for you, but I think you're not done yet ;-)
Also, perhaps CloudFlare Workers are of interest to you. It's a rather new offer in the market. They charge 0.50 dollar per million requests, with a time limit of 50ms per request. Sounds like this combination would work well for you in comparison to AWS Lambda”