Audio sync issue after publishing Captivate project — any quick fixes?

When you preview as HTML on your computer Captivate uses a temporary localhost webserver to display your content.  There is no lag in that case because the audio files are being accessed directly from your hard drive.  However, if you upload your content to your LMS or another webserver, then the audio files are downloaded from the server slide by slide.  The synchronisation issue you mention is likely to be due to the time it takes to download the audio MP3 file and start it playing.  You can test if this is the issue by simply replaying the slide AFTER it has downloaded once.  If the audio synch is perfect on the second playback, then the initial synch issue is due to the download delay.