Can AWS Lambda really be used to host a website instead of an EC2?

I’ve been building and hosting websites for clients for years now. I do this with a CMS and host it in different places including AWS’s EC2. I’ve been reading for years now about using AWS Lambda and have seen some hint at it can be used to host a website. The motive for doing so, is that potentially the cost would be significantly lower compared to running a EC2 instance 24/7.

But is anyone really using AWS Lambda for website hosting? If so, what CMS or framework are you using? What about the latency issue where the AWS Lambda needs to startup before it can serve a web page? I’m not talking about using S3 to host a static website, I’m talking about lifting and moving CMS type of websites to AWS Lambda.

Thanks for reading my preample here. My factual question: Is AWS Lambda ready for prime time to host a website as described, or is this wishingful thinking for the future?