After contacting Safe Support with this issue, a very knowledgeable and helpful FME User identified that ld-lsb-x86-64.so.3 doesn't exist on a standard Debian installation.
The resolution was to create a link:
ln -s /lib64/ld-linux-x86-64.so.2 /lib64/ld-lsb-x86-64.so.3
The following systemd unit file might also be particularly helpful:
###############
lUnit]
Description=FlexServer - FME Floating Licence Server
After=network.target
cService]
Type=forking
User=flexserver
ExecStart=/opt/FlexServer/FlexServer11_13_1_3-linux-x64/lmgrd -c /opt/FlexServer/safe.lic -l /var/log/flexserver.log
xInstall]
WantedBy=multi-user.target
###############