The Thunder Forge

You will not be able to see Wrathion when meeting him outside The Thunder Forge in the Isle of Thunder if you have not completed the solo scenario quests offered in the Isle of Thunder from your respective Horde and Alliance bases there.
If it does not show Unlock the Thunder Forge as completed go to your factions base on Isle of Thunder and search for the non-daily quests that start the solo scenario. This quest requires, to my memory, the first two solo instances to be completed. Later quests in this same chain to unlock your legendary meta will require you to complete all of the solo scenario quests on the island.
I thought this was a bug at first because I couldn't see Wrathion, turns out you just have to complete the solo scenarios first.

Wrathion asks you to meet him on the Isle of Thunder by the thunder forge after you speak to him in the veiled stair. You speak to him in his whelpling form to start the solo scenario.

In the Scenario you have to defend Wrathion while he charges up the thunder forge, you have some shado-pan guys helping you out. There are a few waves and the last wave has a 10m+ hp mogu.

During this there will be blue lightning balls appearing at certain areas and it is marked with an arrow, you go pick it up and you get a buff that increases your damage and healing.

Once you do this part you get to enter the forge itself where Wrathion summons a celestial blacksmith to start charging the anvils to temper the lance. You have to defend the blacksmith from sha monsters during this and you have a celestial defender helping you out. There are multiple anvils and once each one is charged you can click them to deal aoe damage. There are also green pillars of light that appear which you can stand in to heal.

After all the anvils are charged, Wrathion does a massive aoe and thinks it is over but instead summons a sha boss with 30m+ hp.

The celestial defender is supposed to be the tank while you do damage. The boss has a couple of abilities.

-Main one is Insanity which does massive aoe damage and you HAVE to interrupt it or you die. If you click on one of the charged anvils (they all get recharged if you used them in the first phase) it interrupts the ability so make sure you save them.
-Does a meteor shower which will appear as circles on the ground and will follow you around, just dont get hit.
-Banishes the defender for a short amount of time and you gain aggro, he doesn't hit too hard but if you dont want to risk it just kite.

When the sha boss gets low the lance becomes clickable. Click it and use your special action button to kill the boss and the scenario is done and you receive the lightning lance for the next quest. Good luck!

For any healers trying to do this, you don't need to respec for it. In fact, I'd argue it's even easier to do as a healer than as a dps. How? Well, in the first phase, the thunder forge will throw out orbs that will give you the Overcharged buff, which mimics any healing you do as damage to the nearest target. The mechanics here make sure the Shado-pan assisting you will almost always have spare health to heal, so just let them take aggro, stand near a mob, and heal them.

In the second and third phases, the Celestial Defender has a buff on him that increases his damage in proportion to his remaining health. At 100% health, he gets a 300% damage buff (compared to what he does at zero health). As long as you keep him healed up, you'll have enough damage being done to get through. He isn't perfect at keeping aggro off of the Celestial Blacksmith, though, so you'll have to heal it as well. In the second phase, I recommend you don't use the anvils - they immediately reduce the Defender to half health (where he does half as much damage as he does at full health). Watch for the Lethargy debuff on the Defender, which decreases its damage, and dispel it whenever you see it up.

In the third phase, just keep the Defender healed up, kite the Sha during banish, and dispel any debuffs that are put on the Defender. One decreases its haste by 50%, and the other stuns it. Both are bad, but it shouldn't be hard to keep them dispelled. Overall, this phase tends to be easier than the second phase, though, as it's a lot less hectic. Just avoid the Sha's attacks and be ready to use an anvil during each casting of Insanity.