I tried to upgrade my License Server and my Desktop clients to ArcGIS 10.6 from 10.5.1 last week, but I have been getting some strange results. On client PCs with desktop <= 10.5.1, Administrator on client shows all my licenses are available and borrowing is enabled. Once I upgrade the client to Desktop 10.6, Administrator shows no available licenses, borrowing is not enabled, even though Desktop 10.6 and Pro 2.1 on the same client PC start and run normally.
In the attached image, PAUL-WIN10 is a client PC running Desktop 10.6, NSMAP is the 10.6 license server. https://www.dropbox.com/s/p4lcjqyt0h5svx4/ArcLicenseServer.jpg?dl=0
At a different office that I manage, different LAN, this upgrade went without a hitch.