Yes, unless the client's whole system crashes. Assuming communications is TCP, the license is automatically freed immediately. If communications are UDP, then the license is freed after the UDP timeout, which is set by each vendor, but defaults to 45 minutes. UDP communications is normally only set by the end-user, so TCP should be assumed. If the whole system crashes, then the license is not freed, and you should use lmremove to free the license.
FLEXlm applications send periodic heartbeats to the server to discover if it has died.
What happens when the server dies is then up to the application. Some will simply continue periodically attempting to re-checkout the license when the server comes back up. Some will attempt to re-checkout a license a few times, and then, presumably with some warning, exit. There is no part of FLEXlm, lmgrd, vendor daemon or application, that requires root permissions. It is not prudent to run any command, particularly a daemon, as root on Unix, as it may pose a security risk to the Operating System.