Basically, there is a big part of your problem, LFS requires great finesse on the controls, something you just don't get from a keyboard, simply because the keyboard is either full acceleration / braking / steering, or none, nothing in between.
It is possible to be quite quick using a keyboard, however, it will take a lot of practice.
I understand wheels are expensive, in this instance I would suggest you look into purchasing an analogue joypad, you can even use an xbox360 pad if you have one.
This isn't a perfect soloution, but it will give you a good start.