How Do I write an IBM (Lotus) Notes Client?

That's a pretty interesting topic! There are two ways I can think of that provide mail-oriented abstractions, and two that allow you to access mail files as databases directly.

To start out with, and this is very likely the expedient route to take, Domino supports IMAP. It's far from perfect and it's not likely to improve, but it does more or less work for mail access. Not every server has it enabled by default, but it's not terribly difficult or unusual for an administrator to do so.

Recently, the Extension Library has added a JSON-based mail service that purports to provide a pretty friendly API for many operations, but is not complete - for example, it doesn't seem to cover a user's custom views or folders.

Depending on the depth of the project, then there are the routes for accessing the server using Domino's database API, which would be the most flexible but would involve far more hurdles.

The core protocol is NRPC, which, to my knowledge, is only implemented in the core Notes library. As Stan said, it's heavily tied to the presence of an ID file (server or user) and uses that for its encryption. With some setup, you could have that library and ID present and then use the C functions and structs on a platform it supports. This route would give you the most functionality (there are a number of C-level functions to assist with converting between Notes's document representation and MIME).

Alternatively, there is a remote-access protocol called DIIOP that can be used to access a remote Domino server using UN/password credentials via Java objects. This is not enabled for every server, but it's not terribly uncommon, and isn't that hard to enable. You wouldn't have access to all of the C API's functionality for edge cases, but this would cover a lot of ground.