Most things that need to be lubricated usually need to be lubricated again and again. Either it gets dirty, usually from tiny warn-off pieces of metal, and needs to be replaced (oil for car engines), or its substance breaks down under working conditions, and must be replaced (oil for car engines) --or
it simply leaks out and must be replaced (oil for car engines).
Not every lubricant suffers all three fates, but practically speaking, they all tend to suffer from at least one of those fates. It logically follows that for certain applications, if those fates can be avoided, then one shot of lubricant should be useful practically forever.
Now, there are already some things which are labeled as "permanently lubricated", but that doesn't mean that the lubricated things (often shaft bearings of electric motors) aren't going to suffer wear-and-tear and eventually break. Obviously, if we want this Idea to be properly implemented, the lubricant needs to ensure that the parts being lubricated never make actual physical contact; each part must only contact the lubricant that separates them. Note that if the parts stay separated, they can't rub tiny pieces of metal off, and make the lubricant dirty.
Next, if we are not working in a high-temperature environment (such as car engines have), then the lubricant should never suffer breakdown of its substance. Note also that if we can keep the mechanical parts separated by lubricant, then heat from friction is minimized and this possible cause of breakdown of the substance of the lubricant can also be prevented.
The biggest problem may be sealing the lubricant such that it doesn't leak out. It has to stay in place if it is going to keep the parts separated, after all!
Well, I do happen to think we might be able to manage those things. The trick is not just a special lubricant, it's a whole procedure that requires special parts, too.
Most of the special parts are known as "electrets". This is basically a piece of plastic that has a permanent static-electric charge, in the way that a piece of appropriate metal can be associated with a permanent magnetic field.
Let's start with something really basic, a rotating shaft that we want to lubricate and support. Gravity can be a significant factor here, so for now I'll specify that this trick is mostly for light-duty stuff. Advancements in the technique MIGHT someday allow it to be used for heavy-duty things, but for now we'll keep it light.
Normally, at each point where a rotating shaft is supported, some sort of lubricated bearing is used. We only wish to modify the details of that normal thing.
First, INSIDE THE SHAFT, at each support location, we place an electret.
Second, a simple "sleeve" type of bearing will be specified. The shaft does not fit too snugly inside the sleeve; we want to put lubricant in the gap between them, after all!
Third, outside the sleeve, we place another electret. Both electrets must have the same type of electric charge (either both positive or both negative).
Now we design our lubricant. First, we invoke the magic word "Nanotechnology" to create a huge number of very tiny plastic spheres, and each one of them gets a small static electric charge; each sphere will also be an electret.
Second, we chemically attach to each sphere an outer layer of molecules which are basically lubricant-stuff. Because chemical bonds hold these (probably hydrocarbon) molecules to the plastic (also probably hydrocarbon) spheres, they won't break under ordinary stresses.
That's about all there is to our "designer" lubricant. Just make sure the static electric charge here is OPPOSITE to the charges on the shaft and sleeve electrets!
Now we inject this lubricant in between the shaft and the sleeve. Simple static-electric attraction perpetually keeps the lubricant from leaking out! Simple static-electric repulsion helps keep the shaft and sleeve apart, so that lubricant spheres can perpetually stay in-between them, statically attracted by both. And because the lubricant consists of vast numbers of tiny spheres, all of which can "roll" perfectly well, this sleeve-bearing technique should be just as good as, and possibly better than, any ball-bearing or roller-bearing technique for supporting a rotating shaft. --For light-duty loads, that is. Stronger static-electric charges on the electrets may allow heavier-duty application of this Idea. But there are limits to what we can currently make along that line.