Basically, I need to write a Python script that can download all of the attachment files in an e-mail, and then organize them based on their name. I am new to using Python to interact with other applications, so I was wondering if you had any pointers regarding this, mainly how to create a link to Lotus Notes (API)?
You can do this in LotusScript as an export of data. This could be an agent that walks down a view in Notes, selects a document, document attachments could be put into a directory. Then with those objects in the directory(ies) you can run any script you like like a shell script or whatever. 
With LotusScript you can grab out meta data or other meaningful text for your directory name. Detach the objects you want from richtext then move to the next document. The view that you travel down will effect the type of documents that you are working with.
Using Python To Access E-mail (Lotus Notes)