As you can't use the lotus java libraries to access Lotus Domino, your best bet would be to access Lotus Domino via HTTP to get the data.
The simplest way (if you have no experience whatsoever developing in Lotus Notes) would be to try and get the data from the existing views in names.nsf (the Server Directory) and the mail databases. To do so, you can call a view with the following parameters:
http://www.yourserver.com/names.nsf/($users)?readviewentries
http://www.yourserver.com/names.nsf/($users)?readviewentries&outputformat=JSON
In each case you are getting the data from the view "($users)" in the "names.nsf" database, in XML or JSON format.
If you need more data than is available in the existing views, I would recommend against creating new views (as it would imply modifying the standard templates). For that, I would create a new database with agents that recovered de info you need and returned it in the format you prefer.
Agents are just blocks of code (usually written in LotusScript, which is similar to VBasic, or Java). They can be scheduled to run at certain times or events, or called directly (from notes or via URL). You could call an Agent using an url as such:
http://www.yourserver.com/names.nsf/myAgent?openagent
From the agent you could access any data in the server (if you have permission to) and return a "text/html/whatever not binary" to the program requesting the URL.
Note: Lotus Domino 8.5.1, that has just been released, includes the ActiveSync protocol, so I'm not sure about the need to recreate the Notes Client in the iPhone.