This is the effect of shadow copying excluding unmanaged dlls. As you can see from the Proc Mon log, ThomsonReuters.Udap.Bus.Tools.dll (together with all other managed dlls) is copied from the bin folder to the Temporary ASP.NET Files folder, and this is where it's loaded from into the application. Then the process tries to load EikonPipeDll.dll from the same location, does not find it there, tries to find it in the process folder and in the PATH and fails. The reason why EikonPipeDll.dll is not copied to the Temporary ASP.NET Files folder is that EikonPipeDll.dll is unmanaged. There are multiple ways you can go about working around this. Here are some references:
Most likely you're missing one of the dependencies of ThomsonReuters.Udap.BusTools.dll in your build folder. Here's the list of the files you need to have in the build folder:
You may also need Microsoft C Runtime libraries (msvcp120.dll and msvcr120.dll) in the build folder if they're not found in the PATH.
Please also be advised that the data usage rights that come with Eikon only permit the usage of data retrieved from Eikon "for the user's individual use". If you're using data retrieved from Eikon in a Web server application, and you're only licensed for Eikon, you may be in violation of your contract with Thomson Reuters.
You can use a Process Monitor tool to verify the problem.
In Process Monitor Filter, add the web server process, such as iisexpress.exe.
Select only Show System File Activity.
Focus on the file activities for ThomsonReuters.Udap.Bus.Tools.DLL and EikonPipeDll.dll. You need to verify the location of files used by the process to load the libraries.