The white coloration of these animals is caused by a recessive gene mutation* that can only be achieved consistently through certain reproductive scenarios. There is about a 1 in 10,000 chance of this mutation occurring naturally. For lions, a slightly lighter coloration doesn't harm them much-- they are already pretty light in color and live in the open savannah. But for tigers, having stark white against black stripes in the shadows of the jungle is a death sentence. You can't hunt very well if your prey can see you coming a mile away.
Also, white cats stand out more to human hunters, which is always a bad thing.
Of course, when kept in human care these color variations are seen as treasured and rare, and therefore coveted.
In fact, in India, ever since the first white tiger was captured by a Maharajah a century ago, it has been tradition to keep some at the Maharajah's summer palace. But the problem with keeping white tigers (and lions) is that the breeding needed to achieve the white coloration is rather drastic. A male first generation white tiger has a litter of cubs with an orange tiger female. These will all be orange. But if the male first generation white tiger has a second litter with one of his own (orange, second generation) daughters, the white coloration can appear in those (third generation) cubs.
I'm sure you can see where this is going. Inbreeding= bad. Inbreeding, in fact, results in vision problems, hip and spine deformities, kidney problems, and other assorted issues. White tigers aren't healthy and, quite simply, responsible zoos don't breed them.
Now, before you jump up and say, "But I totally saw one at _____ Zoo!" Well, yes. Sometimes responsible zoos display these animals, because at least in our facilities we can give them a good life with access to all the medical care they'll need, and ensure their genes stay out of the very limited pool of the species we are trying to save. But, again, we don't breed them. My zoo actually had a white Bengal tiger until a couple of years ago that had been confiscated from someone in my area. She was much loved by staff and guests alike but her reproductive tract remained unused.
What we do breed are the non-recessively mutated color varieties, as much as we can, responsibly tracking family trees and genetics to ensure inbreeding doesn't occur. Every single subspecies of tiger is currently endangered. Lions aren't yet on the list, but industry people are pushing to get them there. If we don't save these animals now, we may never get the chance. There are, for example, only about 400 Sumatran tigers left in the entire world.
So while I love and admire big white cats as much as anyone, thinking about them mostly makes me sad, and I'm 100% onboard with focusing industry efforts to save the animals we need to. Cats have a mystery and power that makes them enchanting to us, and without them our world would be significantly less beautiful. To editorialize for a minute, I can't fathom for the life of me why someone would think they could capture such beauty by killing the animal. *shakes head* But then, there's a lot that humanity does that I don't understand.
Want to help save tigers? Support your local AZA accredited zoo-- as of 2011, AZA accreditation will only be given to zoos who do not breed recessive mutation cats. And the work most zoos do could quite literally not be done without the people who go there. If you want any more specific sources, feel free to email me or leave a question in the comments and I'll point you in the right direction.
*This does not apply to true albinistic cats, who will have no stripes (in tigers), and reddish/ pink eyes. "White" cats have colored eyes. Melanism (all, mostly, or significantly black) is the reverse of albinism and also not included.