LCCS applications are Flex/Flash applications so you can host them in any webserver / web application server.
If you also want to manage your accounts from your application server we provide a C# server integration module that allows you to create / list / delete room, implement external authentication and also manipulate live rooms and receive events from them.
Check the documentation for server integration and server to server operations. There isn't a C# specific documentation but the C# module is derived from the Java module and there are full javadocs for that.
Also the C# module (payload/serverIntegration/csharp/LCCS.cs) acts as "command line" utility to access your LCCS account via the server integration APIs so you can look at the "main" entrypoint (MainClass.Main) and use it as a reference.
Finally there is a full web application example (payload/sampleApps/Server2Server/DevConsole_CSHARP) supplied with the SDK. It may be more that you need to start experimenting with LCCS because it uses the server to server notification APIs to receive messages from live rooms, but you can have a look at that too.