Assume Earth biochemistry, a thicker atmosphere (1.7 atm) with 22% oxygen and 0.6g. (not sure if conditions really matter, though)
How would a lion-sized, quadruped, land-based, intelligent predator without any sort of flowing-fluid nutrient/oxygen transportation medium survive?
Such a creature is not really viable
The blood transports oxygen and nutrients because the diffusion of such molecules would take far too long to reach all parts of the body. For an organism that big to be viable it would need to actually breathe, drink and eat near everywhere throughout its body. With some suspension of disbelief one could imagine breathing and drinking, but eating is even more problematic. It would have to digest food outside its body and then bathe in it. Even then its body would be extremely porous and might be unable to mechanically support itself on land.
If the creature doesn't have blood to transport nutrients then it's going to need some other mechanism to to the trick. For example, some insects have open circulatory systems, where hemolymph instead of blood moves through interconnected sinuses or hemocoels; spaces surrounding the organs.
Imagine if instead of eating through a mouth your creature spread its food all over it's body so it could ingest it through absorbtion. Mouths are access ports to the digestive system, so if it doesn't have blood to transport nutrients from the digestive tract then it doesn't necessarily need a mouth. You would have to re-imagine the physiology of your creature for this convention to work.
For a predator this could be particularly horrifying if it's routine was to literally bathe in the blood of it's prey; disemboweling it's victims and draping their gore all over it's body; sticking its legs deep inside it's smaller prey to rejuvenate it's aching limbs. Climbing inside larger prey (buffalo to elephant sized) and soaking in all the nutrients it needed. The creature may even have tiny appendages like dexterous villi that move the gore all over and through it's body to effectively distribute it.
The creature itself would probably need a high surface area to mass ratio, it couldn't practically have any one part of it's body be so dense that the nutrients couldn't soak in far enough, unless it used a convention such as insects with the interconnected sinuses or hemocoels; spaces around the organs, but instead of flowing hemolymph through it's body, if flows the partially-liquefied tissues of it's prey all over it's organs using an esophageal action (Imagine the creature had a caustic mucus membrane, or sprayed it's prey with something to initiate the digestive process by partially breaking down the flesh into a usable ooze...). Something else to consider is if it doesn't have blood, or a mouth, then it probably doesn't have lungs either, in which case it would have to stay in motion or in well ventilated areas in order to breath, or it would need to be at least some-what amphibious so it could breath while immersed in a pool of blood or bio-matter. Either way it would be hard to make it a strictly land-dwelling creature.
It wouldn't be a very efficient animal, there's a reason why large animals evolved with the physiology they have now, but in the right environment such a creature could thrive, but it would need a lot of large prey, or it would have to lay dormant for long periods of time like large spiders or snakes. However it turns out though, I think it's going to end up being a pretty terrifying creature.
semi-amorphous slime creature
You need some way to get the food to every part of the body, and to get the excretions out. If you're not distributing it as a fluid, you need to distribute it as a solid or a gas. This involves a decent amount of handwaving in order to make it work in the first place, but if you could make a semifluid amoeba-like creature function at that scale to begin with, you could have it distribute the food packets and purge the waste packets as solids, permitted to pass through its substance.
Your animal is electrical.
https://en.wikipedia.org/wiki/Electric_eel
The electric eel has three pairs of abdominal organs that produce electricity: the main organ, the Hunter's organ, and the Sach's organ. These organs make up four-fifths of its body, and give the electric eel the ability to generate two types of electric organ discharges: low voltage and high voltage. These organs are made of electrocytes, lined up so a current of ions can flow through them and stacked so each one adds to a potential difference. When the eel finds its prey, the brain sends a signal through the nervous system to the electrocytes. This opens the ion channels, allowing sodium to flow through, reversing the polarity momentarily. By causing a sudden difference in electric potential, it generates an electric current in a manner similar to a battery, in which stacked plates each produce an electric potential difference.
So too your animal. Digestion of prey and conversion to energy happens in the stomach and this charges the batteries. Motion happens via electrical energy transmitted to muscle equivalents in the limbs / jaws etc.
2. Growth / development
This seems unsurmountable. One must deliver nutrients to growing organs so they have something to sustain their growth. How to do that without blood? But there are adult animals which do not grow, or sustain tissues, or even eat. Mayflies and cicadas do not eat at all during their short lives.
Your bloodless animal is the adult form. The larval or juvenile is a typical animal with blood, vessels, etc. After it pupates it emerges as the bloodless electrical adult - body grown and not in need of maintenance. Not in need of maintenance and also a short term body, which will wear away in a frenzy of heavy use.
This would make the adult a short term form I think. I can imagine the bloodless electrical adult might serve a specific purpose it its short life. Maybe it is highly charged with energy from its long juvenile period (again think cicada) and kills and eats ravenously, collecting nutrient for the juvenile within its body. It would get worn and tattered in this ferocious process. I am thinking now of migrating adult salmon, who also do not eat but swim ferociously for miles and miles, wearing away their bodies and degenerating in the process.
You might cheat about flowing fluid by saying the osmotic system used by plants is allowable. Technically, that is flowing fluid still.
If that is allowable there would be some osmotic path through the whole body. Could be from the stomach out to the skin. Or could be something like the vascular system. Like stillsuits from Dune, or the plantar cushions of horses, the motion of your organism could be the pump that gives the vascular system extra pressure to carry nutrients effectively. It would mean that, like sharks, your animal needs to move constantly to stay alive.
I'm not sure how you would do it if you insisted on no transport by fluid.
Perhaps the entire body is perforated by tiny tubes. All muscles, even if used for another function like running, slowly contract and relax, drawing in new air and expelling old air. Each tube is lined with alveoli which perform the gas exchange.
You'd have very large numbers of tubes, say one per skin pore. This is a very inefficient design for an animal, since the muscles are diluted by breathing mechanisms, so your predator would be relatively weak and slow. The low gravity would help somewhat.
The brain and other organs would need to be supplied by air tubes that are being pumped by nearby muscles. It's easy to see how this system would quickly evolve into proper lungs - there would have to be a reason that predators with liquids in their bodies don't survive.
[EDIT] I realized this doesn't address the problem of transferring nutrients though... those are hard to transport in gaseous or solid state. Perhaps you could have your predator bring its kills back to a queen that digests the carcass? Then your predator would bathe itself in the nutrient-rich sludge the queen emits, soaking up the energy into every muscle.
But now you also need to have energy storage inside of muscles and organs. Our predator is starting to look less like an animal, and more like an amoeba.
How would a lion-sized, quadruped, land-based, intelligent predator without any sort of flowing-fluid nutrient/oxygen transportation medium survive?
Biologically, it wouldn't. Be it blood, haemolymph or intercellular fluid, it's always fluid that you need. Gas is too rarefied and solid is impossibly slow. And yet you need to get oxygen and fuel from the outside, inside - this requires a transport system, and the only practical means of doing this is a fluid absorber.
So you can have a nonbiological predator - a robot. It could kill its preys, and pulverize and pyrolize them to harvest chemical energy into electrical, then run on electrical power. It would probably also need solar collecting capabilities to supplement its energy requirements.
You would be developing something like a Fourth Variety.
