You can run bitcoind on one machine, and communicate with another over your LAN using bitcoind's JSON-RPC API.
Once bitcoind is running just hit your host machine's local network IP on port
8332 with your API calls. You can find out your local network IP of your host machine by typing
ipconfig in your command prompt.
You didn't mention how you were trying to communicate so let's say for example if you're using Python-BitcoinRPC
from bitcoinrpc.authproxy import AuthServiceProxy
access = ServiceProxy("http://USERNAME:PASSWORD@192.168.2.1:8332")
Make sure you update the
ServicProxy() function with the host's local IP, and your username and password from your bitcoin.conf.