I just tried to find some pics, but couldn't find anything for you regarding the oil lines running around the sway bar, but i'll try to describe the original idea of how they would run. The 90° fittings should face outward in the same direction as the oil filter. The sandwich adapter would rotated to put these fittings to the back of the engine against the cross member (they should have good clearance still however). This does two things: it allows you to secure the oil lines to the cross member and keep them above the sway bar, and allows easier oil changes than having those lines in the way. The lines can then route between the frame rails (with your intake) or below the bottom frame rail and secure to the bottom of it.
The cooler itself originally was suppose to sit similar to
You obviously don't have the same cooler, nor the Nismo brace but you get the idea. Cooler mounting really isn't critical, it just looked like the mounting position put a bit of strain on that bottom fitting. The biggest concern i had when i saw that part of the install was the movement of the sway bar in regards to the oil lines.
Hopefully that helps a bit.