1 - Travel through the caves to reach Lanayru Gorge.
You'll want to land at Lanayru Mines on your return trip to the desert this time. Grapple onto the Clawshot target up ahead and talk to the Goron excavator there about Lanayru Gorge. He's apparently cleared a small hole in Lanayru Caves that should lead there, but he's too small to fit through it. You can find a shortcut to the caves by following the Clawshot targets off to the left, which you can only reach from atop these cliffs. Once you're in the cave, scout out the hole in question and crawl through it.
Unfortunately, the Thunder Dragon is nowhere to be found. Apparently he took ill a thousand years ago and never recovered. You can see his bones rotting up ahead. You'll have to turn back time to get his help, but there's no Timeshift Stone here either. Point your Beetle at the Bomb Flower atop the cactus and use it to blow up the debris blocking the way across to the north door. It's still locked unfortunately, but the key is hanging out on one of the spires in the gorge below. Look for its sparkly surface and nab it with the Beetle, then use it to enter the locked door.
2 - Activate the Timeshift Stone and guide it to the Thunder Dragon's plateau.
There's a minecart with a Timeshift Stone across a chasm you can cross using the Clawshot. Strike the stone and it'll start down the long path around the gorge. Follow it carefully, stepping on pressure switches, fighting enemies, and walking on temporary platforms as you pass them. The first two gates are pretty easy to open, but the third will require you to climb up some vines to the right. That you can reach with the Clawshot. Be quick - the vines only appear while the area's shifted to the past.
Keep following alongside the cart, hopping from platform to platform as they materialize, avoiding the bites of the Babas, and grappling to vines overhead when necessary. Floor switches will appear periodically that open the gates forward - just try not to get left behind.
After the next switch, you'll have to Clawshot over to a long series of vines and climb along the wall. Grab Stamina Fruit whenever you can so you don't tire out, and watch out for a Clawshot target that'll appear across the way. You can use your Clawshots even while hanging from vines, so shoot yourself over, then to yet another target, then drop down to press another pressure switch on the floor to progress.
You'll see a series of disabled Clawshot targets lining the area ahead. They're pretty easy to shoot yourself towards, but you'll have to wait for the minecart to pass by them to use them. At the far end of the room you'll see a patch of vines hanging over the exit that serve as the final target. In this next area you'll fight enemies in close quarters. They're not too hard, but if you're not careful you'll deactivate the Timeshift Stone and sink into the sand, so exercise caution anyway. As you reach the gate, use the Whip to tug on the lever so you can keep going.
The next room will have you crossing a couple long gaps with your Whip. You should be a pro at this by now thanks to the Ancient Cistern. On the other side, there's an electrified gate. Wait for the minecart to pass it by so it deactivates (otherwise beat the minecart to it), then rush through to catch back up. Some Stamina Fruit will keep you from tiring out and getting sucked up by sinksand. Tug on the lever ahead to keep moving forward.
This last room has some Beamos and another lever you need to grab with your Whip. You can shoot the Beamos in the eye with an arrow to destroy it instantly, which is a much nicer way of dealing with them. Once you're outside, follow the platforms as they appear. Bomb the rock blocking the track with some help from your Hook Beetle and make sure you don't get knocked into the gorge by Deku Babas. Like the Beamos, you can just shoot the Babas with the Bow to take them out with no hassle.
When the Timeshift cart reaches the end of the line, it'll charge up the entire area, reviving the Thunder Dragon.
3 - Recover the Life Tree Seedling.
He explains that the robots have tried to help him clear his sickness by planting a life tree across the gorge. Unfortunately, the arid climate has prevented it from flourishing. Now that you've set the Timeshift Stone in place in this area, you can head along the gorge wall towards the sandy falls to the south. You'll find the withered tree on an island in the midst of the flowing sands. Piles of sand hide a nearby Timeshift Stone, so blow them away with the Gust Bellows and turn back the clock.
In the past, the tree is just a little sapling that you can dig up and carry with you to a more suitable location. It'll still need about a thousand years to grow, however. How are you going to manage that?
Life Tree Seedling
This mystical tree was planted a long time ago to help the Thunder Dragon, but when the desert became arid it was impossible for it to grow. Try planting it in a milder climate, perhaps?
4 - Return to the past via the Gate of Time at the Sealed Temple and plant the seedling in the soft soil.
The only place to go is the grove inside the Sealed Temple. Groose suggests you plant a tree there to beautify the place, but since this tree takes so long to grow, you'll have to pass through the Gate of Time to the past if you want it to succeed. Plop the seedling in the soft dirt there and return to the present, where you'll find a fully-grown tree and a massive fruit that you can bring to heal the Thunder Dragon. Roll into the tree to knock it down.
Life Tree Fruit
This mystical fruit took a thousand years to produce, but since it can cure any illness, including the ailment plaguing the Thunder Dragon, the effort was well worth it!
5 - Bring the fruit from the Life Tree to the Thunder Dragon.
From here, it's a simple matter of warping back to the gorge and giving the Thunder Dragon the fruit. (You did activate the Bird Statue, right? It should be second nature by now!) He'll regain enough strength to sing his part of the Song of the Hero.
Thunder Dragon's Song
This is the second of the three songs held in memory by the three dragons of the surface world. Find the final song and return to Levias to learn the Song of the Hero!