frappe_docker is based on DNS based multitenancy
That means the site is resolved from the Host header or X-Frappe-Site-Name header.
Check here frappe/app.py at 66083cece14c532eca047966715fdb5ebff4bd22 · frappe/frappe · GitHub
Reverse proxy in front of erpnext-nginx is needed to override Host or set appropriate header. This may work when only one site is needed on lan.
In case *.lan or *.local sites are needed on LAN then use a DNS server. Set that as primary dns server on machines on LAN.