My company uses Let's Encrypt extensively for many thousands of customers edge devices which live in their own LAN. As long as the hostnames are random or at least not too telling there's pretty much nothing that you're leaking. Except for the internal IP address (10.x, 192.x,) and how many servers you have. If you can live with that then it's perfectly fine.
I wrote about it a few years ago: https://blog.heckel.io/2018/08/05/issuing-lets-encrypt-certi...
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