What I’m trying to do is set up a SharePoint event receiver so that when an item is added to a SharePoint calendar, a reminder is setup in Lotus Notes with the same title/date/time.
I was able to create a Windows Forms Application that creates the Lotus Notes reminder, but when I put that code into a SharePoint event receiver, it doesn’t run. I even tried putting some other code in the receiver that I know works, but with the Notes code in there, nothing runs at all.
Is it just not possible to do this because the Lotus Notes code needs to be run on a machine with a Notes client on it?
Yes, if you are using interop classes, you need to have a Notes installation on the machine, otherwise the DLLs that expose the Notes COM API aren’t there for you to call. And this could be problematic if your SharePoint server is 64 bit, because IBM does not support the COM API on Win64. It can be made to mostly work, but it’s not a good idea to go down that road.
There might be, however, other possible ways to do what you want. Domino can be configured for access via HTTP and supports web services and more recent versions support REST APIs.