Is there any way I can sync my Lotus Notes calendar with a Windows Live calendar?
Not exactly what you are after but I use Awesync to sync up my lotus notes calendars with google Calendar. You can use Awesync to sync to google calendar and then have Windows Live Calendar pull the calendar from Google.
Sync google calendar with Windows Live calendar: http://extremevirtualsupport.com/blog/index.php/windows-calendar-sync-with-google-calendarwindows-live-calendar-with-outlook/
I've made an assumption that you only want to push your notes calendar to Windows live and don't want to edit it. I've also made an assumption that you don't want to move entries from Windows Live Calendar to Notes.
If you want these features then you could consider switching to google calendar and using awesync which will then allow two way sync.
I believe any solution is going to require a 3rd party product and likely using gmail as an intermediary. Check with your companies Notes admins though, they may have a traveler server setup or another suggestion depending on what your specific needs are. 3rd party products have inherent security risks that may be against your company's policies.