Is it not found, or can it not be loaded?
Is there a specific error? Details make a big difference in finding the problem (and a solution).
The 3rd party .NET assembly could be compiled for 32 or 64 bit only (not any CPU). That could be a difference between LV an TS.
Have you tried to load (call any function in) the 3rd party assembly directly in TS? You might get a more detailed error. If it loads, paths are the problem. If it doesn't, something else is wrong.
Are you using the exact same files? Or did you redistribute the files from the LabVIEW system to the TestStand system?
What happens when you call a VI that calls your assembly? If it works from LabVIEW, does it work when you call LabVIEW from TestStand? That could actually be a workaround. Not very satisfying, but still...