Hi,
The server isn't using files from that location. The code is compiled into dll files in the bin folder, but there are also .pdb files (debugger files) and these may indicate the original location of the source code .cs file that existed on the developer machine. So the stack trace shows where in the source code the error is happening and it knows where the source file was located from the pdb file, but the source code is not deployed to production, only the compiled dlls and pdb files are deployed. (deploying the pdb files is optional)
The location of the original source file is not really relevant to the error and is not the cause of the error. The error is about missing file or folder at /Data/Sites/[SiteID]/index ie the location where the files for the lucene.net search index are built. So if for example the folder does not exist at /Data/Sites/1/index you should create that folder to solve the error.
Hope that helps,
Joe