I tried the Jefferson lift and it comes much more naturally to me than conventional deadlifts. But I can't find any quality research on this lift. I am especially interested in muscle activation and risk of back injury.
This is a great question. David Dellanave, a well-known coach, 2012 world-record holder in the Jefferson deadlift, and the author of Off the Floor: A Manual for Deadlift Domination, has a pretty good page has this to say about the "why":
Let’s get the reasoning for doing this awkward looking lift out of the way first. Here’s the short version: because you’re weak. Maybe that’s not entirely fair, but I’d be willing to bet it’s true that you are weak outside the ranges of motion that you’re accustomed to. For most people, these are very sagital-plane dominant squats and deadlifts.
The benefits: doing Jeffersons will help strengthen your conventional deadlift; Dellanave also says it can benefit people with back pain but I don't have any evidence to support that.
I've been doing the Jefferson lift for years. I suffer from frequent sciatic pain due to slight scoliosis, and I find this lift to be the most back friendly of the the Squat/Deadlift type exercises. Would like to see a "Delavier" type comparison between the conventional DL and the Jefferson, but I find it to a be a move I can do with little or back stress.