Been playing for a little over a week and I agree that at first it seems Lightning mains are impossible to deal with early in. My team now looks something like this:
http://prntscr.com/cg8ef9
I just bring along some kind of interruption or focus down the lightning main first. As much as lightning mains cripple your team, taking out their main form of reliable CC on their team cripples them as well.
For talents, I currently take Genjutsu Mirror Return (it increases the damage taken from Ignition while also reversing a debuff put on your team to the enemy team) and for later on I plan to pick up Death Mirage as it basically nulls debuffs every turn (As Aokawa stated). Early game I'd rock out with Sakura if you can, her full heal removes debuffs and makes the fight alot easier against Lightning mains.
I'm still fairly new to the game altogether but I have been doing a LOT of arena since joining the game,
http://prntscr.com/cg8i10
as you can tell, I've not really used many ninjas at all in general and I've climbed pretty high in Arena using this team for the majority of it, its been fairly easy for the most part and I mainly fight against Lightning Mains. I hope that helped a bit.