The latest twist in my DAR work has me looking for the records of the Lyme Congregational Church. I did locate them - and in the process, found one of the best explanations of Lyme's history I've ever seen.
Connecticut towns were usually formed from other towns. To locate your ancestor's records at any point in time, you'll need to know the "current" and contemporary name of the town. If you've ever tried to trace a record for an ancestor who lived in Chatham, you'll know what I mean. It started out as East Middletown, became Chatham, and now, may be Portland or East Hampton.
Lyme's history is equally complicated. Check out this page from the Old Lyme Public Library. While it's not a map, it does just as good a job!