I have heard it stated that the laugh track heard in LITB was not random canned laughter but rather was created from screening the episodes in front of a live audience. Can anyone verify if this is true?

If you go to Wikipedia and search Laugh Track, there is an extensive article. While I didn't find LITB specifically mentioned, I'd guess it has what the article calls a subdued (when describing the example of Courtship of Eddie's Father) laugh track.

Probably the most interesting thing in this article is that the Mary Tyler Moore Show pilot was filmed single camera, and the audio was poor (I had noticed the poor audio). They had second thoughts, evidently, and retooled to multi camera for the rest of the series. Other oddities that I know about (not exactly related to laugh track): Newhart switched from videotape to film after one season; The Odd Couple and Happy Days switched from single camera to multi camera.