Well, kinda hard to answer... a quick google search doesn't turn up much information, the most helpful one was the german wiki: http://de.wikipedia.org/wiki/Lords_%26_Knights
Lucky for me I understand german quite well, but the information contained in it is not much more than what a player might already know. So besides the faint possibility that somebody on this board might work for Xyrality, or might know someone who does, or has worked on a similar game, you will most probably not find out much information about the ACTUAL technologies used for this specific game.
What I can say is that this game doesn't sound to be relying much on "high tech"... if it is anything like travian, it could be built with practically anything as graphical requeirements are quite low.
Networking will need more attention, as this can get complicated fairly quickly (though with the low data load of a strategy game like travian, it clearly is much easier to pull off than the networking requirements for for example an Online shooter, as does the data layer which takes care of persistence.
The "running on different platforms" part though doesn't need that much tech know-how.... you need a backend infrastructure that can talk to the different devices and can handle their specialities, sure, but in the end this can be dealt with by using a standart transportation method that all devices can understand... xml data over UDP, for example... might be byte streams to make it less easy to intercept and read, and most probably some encryption method is used.
So what you have in the end is this
Client (webbrowser, android, iOs) <--------> network <---------> Server (handles the game logic) <---------> network??? (could be on the same server) <------> Data Layer (most probably databases, could be some kind of Big Data)
If you want more details on how this is usually done, I am sure there are blogs and websites on the internet that can give you the technical details.