You would like to know if there is a way of getting agents to update only when they are on a specific subnet or only run when connected to the LAN.
There is no specific setting currently in LanGuard which can be configured to instruct agents only to update when on specific subnets. If agents are installed on the target machines, they update daily at a random time fixed during the installation and, additionally, immediately before each scan.
You can adjust daily updates to a specific time range but not disable them or limit them to a time when the agent computer is on a certain subnet. As for the scan updates, if there is a specific schedule when machines with agents installed are connected to the LAN, you change the agent scanning schedules to weekly scans on specified days.
As a workaround, you may consider asking the network administrator to restrict access to LanGuard server from specific subnets by the network firewall rules, as without access to LanGuard server agent won't be able to update. But the inability to communicate with the LanGuard server will also disable any scanning and patching operations on target machines while they are in the restricted subnet.