Keep in mind that today you probably wouldn't have to light for the level needed for Double-X b&w negative, which is what Willis used for "Manhattan" (he switched to Plus-X to shoot "Stardust Memories" on.)
Roughly there is a large soft box over the dining room area that somewhat backlights him on the couch (judging by the diagonal shadow on the couch coming from the dining room table direction). There is a second soft light over the couch that is less bright, judging from the straight down angle on the shadows under the picture on the wall. You can also see three reflections of lights in the phone on the coffee table that suggest that there is also a soft fill light by camera as the third source.
Now whether he built soft boxes and hung them or managed a ceiling bounce and somehow skirted it to feather the light down along the dining room walls, I don't know, this may have been a location, not a set. It's also possible that the soft light over the dining room table wasn't enough to slightly backlight him on the couch and that is coming from another light hung near the dining room table but pointed at the couch (the diagonal shadow is only semi-soft so it could have been something like from a 2K Zip light.) But the intent of the lighting is to look natural, that there is a soft overhead unit over the dining room table area and over the living room area and that when he stands, he is softly back/top lit by the dining room light.