Haven’t understood your request the first time but now I see that you only wanted NGINX for LAN (which kind of beats its purpose, I think 
). In my opinion, as you still need to type the address, there are more convenient (and some more powerful) ways of dealing with long address names, ranging from simply adding entries to the bookmarks bar to using Muximux, Organizr or Heimdall as homepage and then deal with links to a lot of services (both from LAN and WAN).
Anyway, on the topic: you might want to look at https://en.wikipedia.org/wiki/Top-level_domain as you’re likely have to troubleshoot later issues connected to using .local as TLD because it is used by Multicast DNS.