It depends how you interpret the phrase really need.
If we had had this discussion a century ago, I suggest that most people would have said that many lions live long and healthy lives and produce healthy cubs in the barred cages of city zoos (and even in some travelling circuses), because they have good food, good care from their keepers and good clean, warm, secure housing: so they must have had everything that they really needed.
We think we know better now. We certainly know a lot more. We know about the social organisation and the behaviour of wild lions. We also know that zoo visitors like to see lions in nice, big, beautifully landscaped enclosures (although they may complain if the lions are too far away to see clearly or hidden in the trees or asleep all through their visit). But do we know better about what lions really need?
I think there is very little objective evidence to answer this question, even in species as well known as lions. And we do know that lions are really quite different from tigers, and from jaguars, and from snow leopards . . .
The husbandry of each individual species is a multifactorial problem: animals can do badly in an ideal enclosure if something is wrong with the physical conditions or the diet or the social structure or the way they are managed and so on. The publication of husbandry guidelines is a step forward, in that it spreads ideas from zoos that do well with a species to other zoos, but it is still essentially subjective. Animal behaviour research aim to be objective, but as long as this research mainly consists of short term, small scale studies its value is very limited. The sort of large scale studies like the ones that Marian Stamp Dawkins pioneered on domestic animals might tell us more, but we probably need to do one for each species. Perhaps this sort of question is ultimately unanswerable - but we must keep working towards better answers than we have now.