http://www.awesync.com/awesync.mail.release-candidate
By the way, now it supports and mail sync, too, with Awesync.Mail - http://www.awesync.com/awesync.mail.release-candidate
Soon no need to sync Lotus Notes with mobile devices via intermediary any more:
Prototype of a New Mobile App for Online Access to IBM Lotus Notes Databases (Video) | AweSync
Email Functionality is Almost Ready in New Mobile App for Online Access to Lotus Notes Data (Video) | AweSync
I know the thread is quite old, but... just in case: Awesync (AweSync | Synchronizes your Lotus Notes Calendar, Contacts, Tasks, Notebook with Google, then iPhone, Android & Blackberry)
Actually, it's not exactly pushing and more like one-way sync - Awesync.Mail synchronizes deleted mail, read marks, and it supports mapping between folders. The tool also can work when a Notes client is closed (on a condition that a user is logged in).