So WTF is so great about Lithium?

[Crazy Dazz]

I've been considering the idea of Solar powered batteries for the house.
Basically now in WA the feed-in tariff is a pointless joke. Literally no point in feeding power into the grid.

Obviously the whole concept is ridiculous, but if the government insists on wasting my tax-dollars, then I want my share.

What I can't understand is why they all seem to be promoting Lithium Batteries?
Why?
The principal advantage of Lithium is that it's light, and the batteries provide good capacity relative to weight. That's obviously fantastic when it comes to phones, and even some cars.
But why do I give a rats how much my house batteries weigh??

Even Toyota uses Nimh for their hybrids because Lipo just doesn't last long enough.
And what about deep cycle Lead?