First, a high power fast discharge lithium battery has to be invented, and engineers have been unsuccessful doing it for several years now.
This is one of the things that also makes electric cars powered by lithium-Ion batteries expensive. They must put a large number of expensive batteries in parallel to get the high current rates.
Actually, i've worked with electric cars (more specifically, the chargers for them), and the batteries are all in series, not parallel. The cells are 2.5-3.5 volts or so, in series to make a 12V battery, in series to make about 350-400V or so in the car. Only the cells are made of a few batteries in parallel, think of how many you can fit in 1/4 of a 12V car-sized battery.
Take one 12V battery, and its short-circuit current is about 4000 Amperes. As in, don't drop your spanner, you won't find it again. Or your arm. (Ask a guy called Peter from Valence about that).
There's also different types of batteries. Lithium, Lithium Ion, Lithium Polymer.
Lithium are what your normal AA batteries are, non rechargeable, and probably 20-30 different flavours of chemical inside.
Lithium Ion is what's in your mobile phone. High internal resistance makes for useless in flashes. Only paralleling a few of them into a 3V cell (then seriesing them into a 12V car-sized battery) works for current cars like the Miev and Leaf, but it ain't the best solution.
Lithium Ion-Polymer are the next gen, and stupidly expensive, but they'll be in the next lot of cars once tech improves and the price comes down.
hmmm, back to flashes? problem is, the way they're built right now is with 4xAA batteries in series to make 6V. Put Lithium-* batteries in there, and the recycle will be too slow, they only work as well as the weakest cell, unless they're all together in one pack, with a BMS and can self-balance when they charge.
It *is* possible to make a custom-sized battery pack (like in your camera), even making them 2V or 3V and parallel for higher current, but then you lose the ability to use AA cells, and you'd definitely have to increase the smarts in the flash to monitor the charge level, and you'd pretty much have to bring a spare to any semi-important shoot...