I think the Elder Lions are like Exotic Pets in the Lands Between. They’re very much so not like anything else we encounter on Altus, Liurnia, Caelid or Limgrave, and the places we do encounter them they appear to either be pets or caged. They aren’t native to the Lands Between. Theres also the belief that since their roar and leap seems to have vague storm-like qualities to it that they may be directly related to the true Divine Beast on which the Dancing Lion is based. This holds weight with the fact the Elder Lions are heavily horned creatures - much like the Hornsent - even if some of them have had their horns carved off.
We encounter these lions in multiple spots, but when they’re defeated they do not come back like other bestial enemies (rune bears, the varied fauna, even snakemen.) This implies they are separate from the Golden Order - and thereby not of the Lands Between - as they cannot be reborn through the Erdtree. This is likely because they’re closer to the original Crucible instead. This connection to the Crucible may be the main reason why every single Elder Lion we encounter is chained in some way, and has their horns largely excised - similar to the practice of cutting the horns of non-royal Omen in Leyndell Sewers.
In Stormveil the Elder Lion is off to the side near the entrance. It doesn’t aggro to Godrick’s Soldiers or the Exiles nearby, which implies it may be tamed or a pet. I have a little theory that this Elder Lion is actually Godrick’s pet that he took with him when he fled Leyndell with civilians in disguise. It might have been closer to a cub when he left and its since grown into a giant Lion. Considering where it’s found he probably becomes neglectful of its care later on, likely once he begins Grafting to himself in earnest. But it stays close, and seemingly docile which is interesting and may imply loyalty to Godrick specifically.
In Fort Gael we encounter a caged Elder Lion in the base of the port - almost as though it has been intentionally trapped there. This may be because it was to originally be transported to Redmane Castle but broke free, and was sealed inside by the gate by fleeing soldiers. Or it may be because the Lion was used to train against by candidates to enter Redmane Castle, and is in a sparring pit of sorts. Interestingly this Elder Lion drops the Lion’s Claw Ash of War, which is something we see Radahn Knights and Promised Consort Radahn use. This implies the skill may have been inspired by the fighting style of the Elder Lion (in particular its own leaping downward strike in which it backspins.) which solidifies the theory of them being trained against, or alongside, Radahn Soldiers.
Close to the Sellia Gateway on the way to Redmane Castle, there is a wild Elder Lion, that seems like it might have been injured or be ambushing prey, as theres a lot of Beast Blood on the floor nearby where it hides. It’s quick to fight, which may either imply defending itself from attackers or hunting food. Which would make sense considering the state of Caelid with its giant dogs and crows which all seemingly attack on sight. It’s likely with a broken carriage nearby this Elder Lion might have once been in transport to the castle, but beasts attacked the transport and it was forced to flee.
In Redmane Castle we encounter two Elder Lions together in the courtyard. These lions appear regardless of if the Festival of Radahn is taking place or not, and implies they’re more like guard dogs for the castle than escaped beasts. This is further aided by the fact they don’t aggro to any soldiers or the nearby Page, if either are drawn to the area they roam freely. Considering Radahn’s fondness of lions (due to his idolisation of Godfrey and Serosh) it’s likely these lions are considered honoured pets. And may have even been directly belonging to Radahn at one point.
An Elder Lion is found disguised as a cowering Wandering Noble south of the Windmill Village in some ruins outside of Leyndell’s walls. Considering it drops a Larval Tear when defeated, this could imply somebody tried to sneak their exotic pet out of Leyndell when everything went to shit, rebirthing it as a noble in disguise. The original owner likely perished in the act, since the encounter happens to close to the exit of the gate, and theres no other immediate noble close to the ruins, save those searching for supplies near broken ballista nearby.
We encounter an Elder Lion seemingly in the company of a Perfumer both sitting idly, with the lion sleeping soundly, in Leyndell. With the perfumer actively buffing the Lion, this implies a friendship bond, or a pet relationship, and considering the Perfumers nature and friendship with even Miranda plants from which they harvest this insn’t too farfetched. It may be the Elder Lion was once a nobles pet in Leyndell, but after the city was sealed with golden wax it lost its home. The Perfumer took ownership of the Elder Lion, and cared for it enough that the Lion became comfortable enough to sleep in its new owners presence.
Lastly we encounter two more Elder Lions in Castle Sol. Again, these are reminiscent of beasts once trained against, or reared as guard beasts. They guard the entrance of the castle, where there are no other nearby enemies. A castle watched over by a Veteran, seemingly loyal to either Miquella or Godwyn, and likely related to one of Radahn’s own men as a blood brother due to their similar names and appearances. These Lions may have been sent with Niall, or brought along with his men when he went to Castle Sol originally. As a remnant of his time under Radahn, or as loyal pets. Interestingly, these two have their own unique Frost Breathe attacks. This may be a mimic of Niall’s own manipulation of Frost with his own weapon arts, or it may be the clearest clue of their relation to the Divine Beasts. As the Divine Beasts wielded the power of Storms, of which three types are most common; Winds, Lightning and Blizzards.
It’s possible the Elder Lion and Divine Beasts are one in the same, but I think it’s far more likely that the Elder Lions are Mutt versions of the true Divine Beasts. I think this because of their lack of Storm wielding abilities that we see implied through the Dancing Lion. None of the Elder Lions use Lightning at all, their Wind power of acrobatics is limited, and only two are capable of utilising Frost, which may only be a result of who their master was.
All Elder Lions only drop three items typically; Old Fang, Beast Blood, and some form of Somber Smithing Stone. The Old Fang is rarely-seen and is a vestige of the primordial crucible, solidifying the Elder Lions further as being Crucible beasts. Only two other types of creatures drop such a fang, the Misbegotten and wild Boars. The Beast Blood ‘glints with gold’ and never rots or decays, this implies either being blessed by the Golden Order, or that the creature in question ate flesh blessed by Grace. I think the latter is more likely for the Elder Lions, but the former implies more so to the Mutt concept; perhaps the Elder Lion’s parentage is that of a Divine Beast and of a common beast blessed by the Erdtree? The only two creatures to have a 100% drop rate for the Beast Blood are the Runebears and the Elder Lions, arguably the two most powerful carnivorous beasts we encounter.