In the Avatar world, why are Firebending and lightning generation linked? In Western culture, it seems like air and lightning mesh better (weather phenomena), or perhaps water and lightning (a la Storm from the X-Men?). From a science point-of-view, they're both plasmas, but is there some Eastern connection, or why did the creators connect the two?
Lightning is linked with firebending through many reasons.
But first you have to think what is fire and lightning:
Fire – a state, process, or instance of combustion in which fuel or other material is ignited and combined with oxygen, giving off light (same as the glow of lightning), heat, and flame.
Lightning – a brilliant electric (creates light) spark (fire) discharge in the atmosphere, occurring within a thundercloud, between clouds, or between a cloud and the ground.
Both fire and lightning are linked due to the flow of energy. Fire, when has no fuel, ceases to exist. While at the same time, lightning appears for seconds.
In the Indian culture fire was called Agni, and it had has three forms: fire, lightning and the sun.
In Avatar the Last Air Bender, lightning was considered "Cold-Blooded Fire". And in several occasions (not just in the show), the lightning creates fire when it stuck the surface of a flammable object, let's say wood.
Also, Lightning and Fire burns.
If you want to get into the science behind it, you should look up information on a device called a thermoelectric generator. LSS, in Avatar lore firebenders can turn themselves into thermoelectric generators, allowing them to convert heat into electricity and shoot lightning.
Rub your hands together and they warm up. Friction generates heat. Rub a certain material on shaggy carpet and you can generate an electrical charge. Bring the material close to a conductive metal and a bolt of lightning will shoot from the material to the metal. Kinetic energy can generate both heat and electricity. Theoretically, firebenders can create both heat and electrical charges through channeling energy through their cells or clothing and discharging the energy as fire or lightning.