There is no native way yet to sync Mozilla Calendar (Sunbird/Lightning) with a PalmOS device, but there's a workaround, albeit with limitations. I'm using Lightning 0.3.1 with Thunderbird 220.127.116.11, and a Palm T|X:
Part I: Use Google Calendar as your base, and sync it with Mozilla using GCALDaemon
1. Get a Google account and set up a Google calendar. This is going to become your Lightning calendar, too, so if you've already entered stuff in Lightning, export it as an iCal ics file, and import it to Google so they match.
2. Set up GCALDaemon using the http method and, in Lightning, subscribe to your Google calendar through GCALDaemon as described in GCALDaemon's user guide. Now changes made in Lightning show up quickly in Google; changes made in Google show up within 10 minutes in Lightning when you reload remote calendars.
Part II: Sync Google Calendar with your PDA using Goosync
3. Get a Goosync account, install it on your PDA, and use it to sync up the calendars (I do it via wifi on the PDA). Anything(*) you put into your PDA will get sent to Google and vice versa.
(*)Actually, free Goosync only synchronizes events 7 days in the past and 30 days ahead, so if you plan to schedule events out farther than a month and need to know about them consistently, you probably want to pay for the Goosync subscription service, which gives you a 365 day past/365 day future window.