Something like unreal engine 4 would do the job well as it already has industry proven LODI have no real experience with unreal engine 4 so I was wondering exactly what you mean by this? Does UE4 use some sort of dynamic LOD or is it still static but the method used to select LOD level is "robust"?
Well, I am sure most proven engines would work. I point this out because selecting something premade simply means that a lot of edge cases that can go wrong have already been found and fixed, and all the development is done for you. When you're dealing with something as large and complex as an open world game, IMHO you need as much of a leg-up as you can get your hands on as producing the content and populating the game world will be challenge enough!
I speak from experience as I am currently making an open world game myself and I knew from the start that it would be content that I would need to concentrate on. Without content an open world game is just an empty wilderness for the player to get bored in :)