I can't really comment on how to fix it, but I'm looking at it from a programmers perspective. The exception the log is telling you is that the file "AdvancedHook.dll" is missing as an assemblyreference. I don't know enough of c# (csharp - language this software was programmed in I suppose) or .Net to tell you that you are at fault here or the software you install lacked the proper parameters to include the file automatically.
I would try to find the AdvancedHook.dll assembly online and include into the script folder in gta iv and see if it helps. A quick and dirty Google search on advancedhook.dll got me redirected to >this script. Try installing it and see if the problem solves itself.
EDIT: I am installing LCPD First Response right now as we speak, and I can see the advancedhook.dll is automatically installed with the installer. Are you running version 0.95 rc2 of lcpdfr or 1.0b?
Installer pic with advancedhook: '>