Does this happen with other games too, or is this exclusively with LFS? Try other graphic intensive games and see if you get the same results. If it happens with other software, then I'd say it's more likely a hardware issue.
If the CPU is good and is running cool, you may want to check that Direct X is running alright, in particular Direct Draw. You'll find a DXdiag utility in the Direct X folder which is part of the Windows system. I don't know if DX is needed for LFS but the thing is that DX loads automatically when Windows starts.
If that proves ok, then run the diagnostics on your video card. If you are running on Windows XP then try to download the latest XP drivers for your video card. Microsoft has launched a series of new patches for XP and it's possible that if your video drivers are kinda old (like mine were) they may not be all compatible with these patches.
If all that is alright, then you may have to check all your hardware, one by one. It's a long and tedious process but it's better than buying a new puter. My puter was crashing at random and it was a bad keyboard. But it took me a week to figr that out.
Good luck