First things first : it seems to me that you are trying to make Notes do something that it was not designed to do. You don't have an SQL db here, you have a document-centric db which does not pay much attention to real-time operations.
I used to be a certified Notes instructor, specialised in the Developer path. Back when I did the courses (R3, R4 and some R5), I always started the initiation course by outlining the things Notes can do, and those it cannot do.
One of the examples of things Notes cannot do is a real-time airline ticket reservation application. It looks like you are interested in real-time process tracking. The keyword here is real-time, and Notes does not like that.
Therefor, before you go to far with this, I strongly suggest you either cut real-time out of the picture, or redefine yor expectations to allow for post-processing measurement.
Now that I have been suitably pessimistic as to your chances, some encouraging words are in order :
In a Notes application, it would be logical to put code in the button the user clicks on to indicate the end of the process, and have that code calculate the difference between the arrival date-time and the current date-time, sending the result as a message to somewhere.
One other possibility is setting the Delivery Options to return a notification on delivery of the mail in the mailbox - however I find that to start a process directly when mail is delivered, without ensuring that the user reads the mail at that very moment, is not fair. Starting the process with a Return Receipt would be a lot better - at least you know the mail has been opened. Even then, you might want to look over the client mail query interval setting, and whether or not the user uses the Preview Pane and the settings associated with that.
Actually, the best way I can see for the moment would be to create a db with a formal process defined in a form, create a new doc for each process to be run, and send doclinks to those users who are in charge of handling the process.
That way, you centralize all information in one place. You can record when the user opens the document - thereby starting the process. You can have the user click on a button the indicate the end of the process, thereby allowing you to calculate the time interval with reasonable exactness. Finally, you'll have a single-storage db of all pertinent info, instead of having process info spread out over a number of mail dbs.
I suggest you think about this for a while, and come back to give your opinion on my solutions. The community will certainly be able to evaluate the best solution for your needs.