I finally found Lula Lake and visited it on a late October Saturday. It is, indeed, east of Cloudland Canyon State Park. It is on the eastern brow of Lookout Mountain, on Lula Lake Road, perhaps 10 or 15 miles south of Chattanooga. It is owned by the Lula Lake Land Trust and is open to visitors on the last Saturday of the month. I was amazed at how pretty this place is. I thought I knew just about every outdoors destination in north Georgia but this one remained "under my radar" for many years. It has two falls and a canyon. On the beautiful fall Saturday that we visited, the place rivaled Cloudland Canyon. The chasm isn't quite as large, but the lower falls are bigger than either of the two in the state park. There are many hiking trails and a very nice vantage point overlooking Chattanooga Valley. A place worth seeing.
If anybody has any information about the 1950s double murder that took place there, or the little coal mining town of Durham, I'd be very interested.