No. There is no part of FLEXlm, lmgrd, vendor daemon, or application, that requires root permissions.
It is strongly recommended that you do not run the license server (lmgrd) as root, since root processes can introduce security risks.
If lmgrd must be started from the root user (for example, in a system boot script), it is recommended to use the su command to run lmgrd as a non-privileged user:
su username -c"/path/lmgrd -c /path/license.dat -l /path/log"
Here, username is a non-privileged user, and path is the correct path to lmgrd, license.dat and debug log file. You will have to ensure that the vendor daemons listed in /path-to-license/license.dat have execute permissions for the username. The paths to all the vendor daemons in the license file are listed on each DAEMON line.