That's an NP203 where the main output shaft cone has been put on upside down to exit the speedo cable to the passenger side.
Straight-weight 30W engine oil is the correct lubricant.
Note that if that is a modded NP203 and you have locking hubs (rather than slugs), and you drive around with the hubs unlocked, you must lock the transfer case once in a while to throw oil up inside the case so it can run down the internal rails into the oil reservoir at the main output shaft bearing. If you do not do this, you will end up running that bearing dry and eating it up. I lock the transfer case for the first mile or two I drive every day, then unlock it for the rest of the day. If on a long trip, lock it for a mile or two every time you start out after stopping for gas or a rest stop. Note that, with the hubs unlocked, you can only lock the transfer case when stopped, but you can unlock it when moving.