First, depending on what you are gearing for, let me save you the trouble and say you are much better off going with Fire or Arcane. Lightning is really only viable for up to T4. T5 and T6 are doable with Shard of Hate, but they're at least twice as slow farm wise. If you just want a change of pace to play lightning, it can be fun for a little while.
As far as your gear, well, there is a ton of room for improvement. You need to stack as much lightning damage as possible, ideally ~86% or so is the ceiling for lightning. Andariel's should have those type of rolls, but with the +lightning % on it. Your neck could benefit from +20% lightning damage legendary and you really need a Stone of Jordan. You should be seeking a glove with tri-fecta stats on it as you really need crit damage on them. Try to increase your gems as much as possible, since Wizards benefit hugely from +int gains. With this in mind, for lightning, you should be looking to benefit from 2 piece Firebird and 2 piece Vyr's set bonuses for the int gains. Aughild's also isn't bad for the +elite% dmg bonus (since you don't have Unity or SoJ). Basically, go with crit damage, crit chance, and attack speed. When properly geared, most of your damage will come from Electrocute or Shock Pulse (with Shard of Hate), so attack speed is very beneficial. Fulminator isn't really that great of a weapon proc, so ideally you'll want to replace that with whatever higher DPS weapon you find. Shard of Hate is the best for a lightning wizard, however Thunderfury works well too.
It also seems like you're trying to make up your toughness mostly from gear choices (like the All Res on your neck) when Wizards have the best skills in the game for this. Unless you're trying to only farm T1, there's no reason you shouldn't be using Energy Armor/Prismatic Armor. Unwavering Will is also really great to have and should replace Evocation (no real point to this as a lightning wizard). Not really sure of the major benefits for Astral Presence, but try using Prodigy instead.
And for proof,
here's an older video of one of my lightning wizard builds before Shard of Hate.
As I said, it is fun to play as a change of pace, however it's not nearly as effective as Fire or Arcane.