It would take several dozen generations, perhaps 100's. You have to cull out the less tame lions at each step, that's how the genes are selected. At the same time, you need to keep the species healthy; it might be impossible to have a tame healthy group of lions.

Similar things have been done. You can now buy a "pet Arctic fox" from Russia. I don't know how many generations it took but they used selective breeding to produce foxes with 'compliant behavior" so that, rather than panicking and trying to rip the humans to shreds, the fox allow themselves to be picked, petted, fed by hand, etc.

Of course, a fox is probably genetically closer to it's domesticated cousins than a lion is to a house cat.

I'm not asking about one individual animal, but just a species in general. Lions are the first to come to mind.

Now, I understand that a social canine is far easier to deal with than a mighty big cat. But I'm just bringing up dogs as examples.

So, foxes have been bred to nicer foxes and so on to produce domestic foxes, and their genes cause them to slowly gain the characteristics of a dog. And then you have fennec foxes...they're also bred in captivity. They started off wild and now are "partially" domesticated. They are less skittish around humans than their wild cousins and can even be litter box trained, but they still look like a fox.

Under the assumption that breeders gathered a handful of lions--whether they be wild or rescues--and bred the most docile of these lions together for some generations, how long would it take for the lion to become somewhat domestic? Not as in just a wild animal that you slap a collar on and call a pet. That's just mean and stupid. But an animal (species) that has lost it's fear of humans and sees them as one of their own...like your dog?