The simplest way is to use the COM interface of Lotus. If this application is specific to a user, then you can use the client information on their machine to make a connection (NotesSession object). If it is to be run on a server, you must install the Notes client on the server with a separate Notes.INI for the COM methods to work. There is lots of documentation out there on this, even in the Designer help. But feel free to ask more questions if you need help.
Another option, if you want to go this route, is to configure a Webservice consumer in C#, and configure a Webservice server in Domino that will then use basic LotusScript functions to reach into users mail boxes. Either will work, the former being the fastest, the later taking extra time but perhaps being more desirable.