During the installation of LF Server, a Service Connection Point (SCP) is added to AD for the LFS. Note that if LFS runs as the System user, it also creates the SCP at service startup if it is not found in AD. The clients use the AD SCPs to find LF Servers on the network. Since both networks are SubDomains with a trust between them, as long as the SPC is published, both domains will pick up the LF Server.
You can Set LFS to run as a Domain account and then remove the SPC (preventing any client from auto detecting it), and then use Group Policies to push out the Repository registrations to the users that need them.
See Managing Service Connection Points for information on removing the SPC
See Roberts reply in Manually publishing a service connection point in Active Directory for information on pushing out the needed Registry settings through Group Policies