There is a simple answer to this question.
The biggest gain you'll get from LFS or any race sim is racecraft: spotting danger, making snap decisions on how to get through carnage, recognising when something is going to go very wrong before it's too late and learning how to pass difficult people.
I've been away for a couple of years so hopefully the following no longer applies, but previously I found that LFS was never accurate enough to be relevant in real life.
It could certainly teach you the basics of car control; response to spins, coping with weight transfer etc., but the finer elements of driving can only be gained by experience in
that car on that
track.
The problem with karting in particular is that it's such an incredibly responsive machine, driven on instinc, and I think it's just too hard to recreate in a sim. Driving an MX-5 (normally a responsive car) after going karting is always a huge disappointment as it feels wallowy, sluggish and unresponsive. It's the only bad thing about going karting