There's plenty of Dumbo-esque cuteness in director Lisa Leeman's documentary about an elephant, Flora, and her circus-impresario owner, David Balding. Leeman originally set out to make a feel-good tale of Flora's retirement from three-ring life---Balding planned to place his adopted pachyderm in an African reserve in 2000---and you can see remnants of that movie throughout. (A few too many reaction shots of children in doe-eyed awe; a quirky musical score that sounds like it's trying to coochie-coo audience heartstrings.)
Thankfully, life took Leeman and her crew down more-interesting paths---nearly a decade's worth. For a variety of reasons, Balding's Africa plan falls through, and he has to search for another home for his five-ton pet. The ideal location is the Elephant Sanctuary in Tennessee, a sprawling habitat where Flora could roam freely, and where she is finally admitted in 2008. This is where the doc gets really intriguing: Balding deals (none too well) with separating from Flora; the creature goes wild (to the point that she's diagnosed with post-traumatic stress disorder); and we hear fascinating testimonies about whether the animals are more emotional or instinctive creatures. That One Lucky Elephant ultimately comes down on the side of anthropomorphizing Flora and her kind is extremely disappointing---a little clear-eyed ambivalence would have helped the film feel more focused and less like patchwork.