In Bastian Sick, "Der Dativ ist dem Genitiv sein Tod", I read that it is "stilllegen", but "lahm legen". He didn´t understand it himself and did not give an explanation, why the first word is written in one, whereas the second has to be separated in two. Can somebody explain?
Since you don't provide the context, it is hard to tell.
But I think the main difference between the two is that lahmlegen means to bring something to a halt temporarily and stilllegen means to shut it down permanently - for example:
Er legte den Verkehr lahm.
means that the traffic is blocked for some reason but it may continue after a while
Er legte den Betrieb still.
means that the factory was given up and it will not continue to work.
As Takkat pointed out, I may have misunderstood the question - are you referring to this ? I'd say Bastian Sick gave an answer himself there (since he maybe published the book earlier).
Although, the Duden also writes lahmlegen in one word.
I think there was some confusion caused by the spelling reform. The Duden writes it as one word:
The general rule is if you can have a comparative form of the first part, it's written in two words. But it looks like this rule is only applied if this comparative makes sense in the context of the word, e.g. you have "lahm", "lahmer", "am lahmsten", but if something is "lahmgelegt", it is stopped and you can't stop it even more.
That said, you'll find inconsistencies of this kind a lot. The Germans (including me) are confused about this topic as well, as the spelling reform was adapted several times. The matter gets even worse if both versions have a different meaning, e.g. "auseinander setzen" and "auseinandersetzen": You use the first one when two kids fight and you don't let them sit next to each other because of this, and the other one means "to deal with, to argue with, to discuss". You can imagine the chaos when the spelling reform tried to touch some of these constellations.
I read the books of Bastian Sick as well, and they were quite entertaining, but you should take them with a grain of salt. You'll find a lot of (sometimes quite elaborated) criticism in the blogosphere.