This is how I would do it:
Add a hyperlink column to the Document Library
Add a 'New Item' event handler to the DL which adds the url to the hyperlink column, and point the hyperlink to your own ASP.Net page (or even the DL itself), with details of the document required (ID et al) in the GET string. Call this hyperlink 'Request Access' or something similar.
Create a webpart which checks the GET string for the right variables, identifies the user (currently logged in user viewing the page the webpart is on) and sends you an email informing you of the request. Add this webpart to the target ASP.Net page in step 2.
When a document is added, the event handler will update the hyperlink column with the required hyperlink. When a user requires access, they will click on the properly formed hyperlink, which will take you to a page with the receiver webpart on it. The receiver webpart will get the required information from the GET string, inform you via email, and also inform the user that the request has been received.
Although I'm sure theres a better way to do this...