The drivetrain carnuck is considering operates in the the opposite direction of what one could consider 'standard', rotation is opposite of what is in his Eagle now. By flipping a rear axle his goal is to use it in the 'reverse' direction as it is designed to operate thus matching this new diesel powertrain.
Yes, pinion bearing lubrication would be a major problem. This has been done on other types of rear axles but this issue had to be addressed. Skip it and the axle won't last long. I believe to resolve it in other applications new oil passages had to be drilled since the original passages were located on 'top' after flipping. You might start researching this on another web site that is known for having a lot of pirates and 4x4 vehicles. If you haven't been there, and if you post questions, the atmosphere there is the opposite of the Eagle Nest forum. Here everyone is friendly and there are no dumb questions. Over there most everyone is...not so friendly.
Another consideration is that your ring & pinion will be operating on the otherside of their teeth, what is considered the coast side, which is the weakest side. If you didn't push it hard you could get away with it. But since the factory rear axle is based on the Dana35, a notorously weak axle due to a poor ring-to-pinion ratio and small contact patch, I'd be concerned with strength and longevity.
The brake backing plates could be flipped from side-2-side, so your parking brake cables should be fine. You'll have to move your brake lines. Not a major task but one to list on the to-do list.
You'll want to scrutinize your driveshaft angles. Someone on here may know for sure, but pinions are seldom perfectly centered. They are intentionally offset to allow for a few degrees of driveshaft angle so as to allow the u-joints to run in sync.
If you can resolve the pinion bearing lubrication issue you could pull it off. Just have to make sure the squeeze is worth the juice.
One more option I'd like to mention is using a front axle and turning it around to use in the rear. It comes with its own challanges such as the pinion is off-set far to one side. You could retube the pumpkin but it isn't cheap to pay someone else to do it. You could do it yourself if you have the equipment. You'd have to decide if you want to solidly lock the steering knuckels in place somehow, build it for rear steer (dangerous on the highway), or remove the knuckels during the retube process and find an axle bearing that will fit the larger front axle tube. I'd go for the latter if I had to choose. Or you cold not retube it, use it as is, and get a tc with a passenger side offset. Problem there is that your front axle wouldn't line up then...unless you flippped it too.
If you are dedicated to such a build, my hats off to you as it would be a major undertaking.
What kind of application did this diesel drivetrain come from? You can't get a rear axle with it?