relocation error: filename: symbol errno, version GLIBC_2.0 not defined in file libc.so.6 with link time reference.
The executable is third-party's version of lmgrd, the utility that starts their license server.
That executable must have been linked on an ancient machine. Here is a good explanation of the problem.
Is there a way I can add a patch myself to the source of glibc and fix this problem locally on my machine alone?
Yes, but you really shouldn't do that (it's (a) complicated, and (b) you can easily render your system unbootable if you screw up your glibc).
Contact the 3rd party vendor and tell them that you can't use their product due to broken lmgrd
. Ask for your money back. You may be surprised how motivated they may become trying to solve this problem.