Just after we had our main Domino servers in the office upgraded to 8.5.1 FP1 I looked into doing to Lotus Traveler configuration updates required to be able to process calendar invites on the iPhone. I did the changes, restarted Lotus Traveler but were unable to see invites on my phone. I messed a little around with it but with no success. Today however I heard other iPhone-enabled colleagues mention that they processed invites on their iPhones. WTF!!
Tonight it hit me why. I have been using the Notices mini-view in my Inbox to show calendar invites for easy processing. Having invites show up in the mini-view apparently blocks the invites from reaching my iPhone because after disabling the use of the mini-view in the mail preferences and sending an invite from my private e-mail/calendar system the invite appeared right away on my iPhone. So there it is - problem solved.