the server makes a GET request
Is there already a library that implements this with the core functions available on the Arduino? (read/write Digital / Analog, read 1-Wire temperature etc.)
I've found a WebServer Library  that allows to attach request handler functions to URL's.What has to be done is writing such request handlers for all the arduino functions.
Servers don't make requests. Clients do. Servers respond to requests.
All the libraries are available. What you need to do, if the Arduino is to be a server, is parse the GET request, and serve up the requested page, calling other library functions, as needed, to get the data required to service the request.
In general, the WebServer library is overkill, since the Arduino is already serving some purpose for which you want the data to be available from the internet. Possibly, you want to control some stuff from the internet, too.Get more specific about the Arduino you have, what is connected to it, what you want to expose to the world, and what you want the client to be able to do, if you need help doing something.
I don't want to reimplement this software for the arduino. Instead this program should run on the server and only the parallel interface part should be replaced by the LAN protocoll to the arduino.
What I've asked for is if there is a webserver that implements the core arduino functions.
I want a library that can call the core arduino functions (digitalRead, digitalWrite, etc) by LAN.
and the seperated server which controls the arduino by LAN.
Removing all the unnecessary noise...
QuoteRemoving all the unnecessary noise... So, if the first reply you got was a simple, terse "NO", you would have been happy?
there is at the moment no ready to go library that implements a LAN interface to core arduino functions (digitalRead, digitalWrite etc.).
I think firmata does something like what you are asking for - you can control and configure the board from a host computer. There are various implementations for using it over ethernet around, but I think they are all fairly old, so may not work with the most current version.
I had to do something similar with my Arduino controlling my Christmas lights. I suggest making the commands you send to the Arduino single