Then they architected and built it out wrong.
It's pretty simple to run low cost services in AWS. If you're small enough that an $800 desktop on a home internet connection will handle it, surely you could run it completely serverless for much less.
I'm surprised how many people I see wanting to go on-prem vs AWS/public cloud. Feels penny smart and pound foolish to me. Lots of people too deep into the technical side of things that they don't even understand the business side.
You vastly underestimate what you can do on prem. Equivalent elastic compute for a $800 desktop that uses $100/mo in electricity is >$2000/mo. As sibling points out, it could easily be much much more depending on what you're doing.
Bandwidth is usually the killer with AWS. Bandwidth on prem is free. Some cloud vendors are much better, in fairness.
Hard to say. A $800 desktop could easily equal the compute of $100k/mo in lambda costs.