I think this requires a quick lesson in how LFS replays work.
Unlike AVI files, or MOVs, etcs LFS' replays are the inputs from each driver saved in sequence. What this means is that its not an actual video file, but merely a file of commands that tell LFS what to do when it reads the file.
What Fraps does is record on-screen action.
With this in mind you should now understand how to use Fraps and record a video following the above instructions. Bear in mind that you need to tell Fraps when to start recording. Also bear in mind that Fraps creates huge uncompressed files.
If you understood that, I apologise, but telling us it "doesn't work" isn't a very good explaination.