This is a very interesting fact on it's own. Can you speculate more on why they can interbreed despite being less related to jaguars and leopards, or maybe they can interbreed with leopards and jaguars too, but no one has tried to do that....maybe they would fight too much or something?
I think you may have get the relatedness a bit wrong, but I'm not sure if you did, so I'll restate, just in case. Lions are more closely related with leopards, then with jaguars I think, and only then with tigers. Nevertheless, hybridization is more successful with lions and tigers, more specifically, with lions and tigresses, and not so much with tigers and lionesses.
It's reported that lions can indeed generate hybrids with leopards (and perhaps with jaguars), but it's just far more rare by some reasons, first of all, species tend to mate with members their own species, obviously, so it would hinder natural occurrences*. Secondly, in captivity, they'd presumably be more often kept separated than lions and tigers due to the larger size difference, so leopards would be safer and under less stress. Thirdly, and perhaps the more meaningful here, possibly there are more relevant differences in the embryological development of leopards and lions than there are between lions and tigers, of similar size.
To illustrate, I'll briefly explain why hybrids between lions and tigresses are more viable than the hybrids of tigers and lionesses: in the production of the gametes, there is one process called methylation, in which the expression of certain genes is hindered by a "chemical lock". Males and females will sometimes "compete" with each other using these chemical locks. Males can have more multiple sexual partners than females, often at a considerably lower cost (as the females are the ones who get pregnant and often do most of the nurturing of the offspring). They can have fitter offspring if they could have gametes that would instruct the growing embryo to develop as much as possible, to suck up the resources of the mother as much as it does not backfires (she must be healthy enough to giver birth to the offspring and nurture it effectively). It is actually done by the males with these "chemical locks" on the gametes.
For females, in the other hand, they would benefit if they have gametes that would counter act that, instructing the embryo to take easier on her, so they could recover more easily and have better chances to eventually have more offspring with another mate, or at least be healthy enough to nurture better the current offspring itself.
When a males have access to multiple females, and the females are related and social, as in the lion's pride, the strategy can be driven to an extreme. The lion's gametes will instruct the development to exploit the female to the maximum, as the threshold of viability is stretched; the bodily resources of each female can be more exploited. Even if a female is exhausted and weak after giving birth, her sisters, older and younger ones, which hadn't gave birth exactly at the same time, will help taking care of the young.
With tigers, that does not happen. So the sperm does not instruct the "cheat" the embryo to grow the most. The ovum also does not counter act this "cheating", so the offspring will be a healthy tiger cub. But if a tiger sperm fecundates the egg of a lioness, then the embryo has no much emphasis on growth from the sperm, and many growth restrictions imposed from the lioness' egg. Then the result will be a weak "tigon" cub, which if survives the whole development and reaches adulthood (which is rare; apparently they often die on the development itself or short after birth), will have a smaller body size and shorter lifespan. In the other hand, when you get the sperm of a lion, with plenty of instructions to develop as much as possible, and the egg of a tigress, without the counter measures for such exploitation, if the pregnancy is successful (not as uncommon with tigons, I think), she will giver birth to a "liger", which, if reaches adulthood, will be bigger than both parents (the biggest cats alive today are ligers, even though some are overfeed in order to exaggerate their weight), and may even live longer, I think.
A similar process may restrict even more drastically the success of hybrids between lions and leopards, but perhaps driven by "real" genetic differences (not just epigenetic/methylation). The gametes of each species may have growth instructions that don't fit conjointly, and also perhaps there is different gestation times for each species which would only make the whole thing even messier. But perhaps would not be so troublesome with tigers and leopards or jaguars, but I don't know of any case of hybrids between these, while there are at least one allegedly case of hybrid between lions and leopards.
One could test the idea by impregnating them under medication....but cruel, but still, it would be interesting to see?
I don't quite get which medication you have in mind. Anyway, perhaps it's not done because scientists actually know better what's going on and don't have anything interesting to learn from that. And perhaps a similar principle could be tested with, say, mice and rats, or some fish species, something more suited to the lab, with less ethical implications due to the rarity of the species and all these things.
* Not so much as the natural occurrence of lion-tiger hybrids is hindered, as they almost never coexist in the same habitat, lions are mainly african, and tigers are mainly asian. They do met in India, even though I think that lions still inhabit savannas there while tigers live in the jungle. But species are probably rare there, if not extinct already anyway)
™ Version 4.2
