Saw an early screening of this and I have to say that Adam Arkapaw did an excellent job on it. It's obviously shot with some sort of older, or perhaps even coating-stripped anamorphics. Sometimes when people sit in front of window or bright background, they almost disappear in the veiling glare they produce. An interesting look that works well if you don't mind losing your subject in the glare at times.
Very naturally lit (as is the trend at the moment), but with enough flourishes and nuances to make it interesting and not full documentary. Tasteful and skillful. There is particularly a shot that I love, where Fassbender's character, holed up in the lighthouse, is composed so as his face and body covers the lantern lighting the room behind him. Very impressionistic. I absolutely love when the source of a light is somehow obscured in frame, ideally by the actor. It's much more interesting than having a source in shot I find many times. In fact, I've recently become allergic to having practicals on. It became such a trope that every single practical has to be on, no matter if it's day or night. It's been done to death. I'd rather have the shape of the lights or shades, but not have them on.
There's also a night storm sequence when his wife is trying to reach the lighthouse that is very well done and lit. You can tell they had to light from the ground here and probably weren't able to light from high above to emulate moon, but the DP turns it into an asset and makes the scene much more dramatic because of it. Beautiful work.
Film is overall excellent as well. A sure Oscar contender. Only complaint I had with visual approach is that it was a mix between static/tracking shots and very handheld stuff. Never really understood why.