He never mentions what memory provisioning he uses for his lambda but he does remarks that he has 10M requests a day and that'll cost 10$ a day in lambda costs. Which comes to 0.000001 per request. That puts his service at 512MB memory at 0.000000834 (+ 0.0000002 per request).
If instead he used a 128MB instance (which is reasonable if your request is 3ms, but probably not enough to run .net core) you'll be at ~0.0000004 . Which would put it at roughly half cost. At about ~120$, which is the same as his server setup.
He did mention that he could cut his costs by reducing memory usage.
Seems like there's no reason why it couldn't match up to the server-side cost. I don't think the cost-benefit analysis is as bad as he makes it out to be.
Seems also like there's a very big mismatch in pricing here. If his workload is about 3ms per request but he is charged for 100ms a request, then that's a 33 fold increase in pricing compared to being charge per millisecond. Seems like quite an opportunity for some cloud provider to differentiate itself.