"Frodo is exhausted with the travel and cannot jump or dive roll anymore. Unfortunately there's still one climbing waiting for him. First you have to head to the right and break two crates found there. Build a footbridge from their pieces which will let you move onwards.
Take out the Phial of Galadriel and light the nearby cave. Afterwards push the stone towards the river of lava and dig up the ground with Sam. You will obtain a rock which you can throw into the support on the other side of the lava river, completely blocking it. Now you can move further to the right.
Avoid the fire traps from the prologue and you will reach a rail. Trying to use them to cross the river will fail, though thanks to moving the stone wall, platforms will appear from time to tie on the river. You need to time your movements right and use them to get to the other side.
Break the gate in front of you, switch to Frodo and enter the darkness. After getting to the other side of the cave, Sam should use his rope to turn over the pillar and therefore create a bridge.
Once again use the "elevator": Frodo should stand on the lower (right) platform, while Sam jump onto the upper (left) one. Switch to Frodo and destroy the stone above to create a bridge. Now place Sam on the right platform and Frodo on the left. Switch back to Sam (he should be above), jump across the chasm above the river on the right, dig up LEGO bricks and build a bridge for Frodo.
Use the elven rope on the hook and move to the right, therefore reaching another "elevator". Frodo should stand on the right side and Sam use the rope to reach the left platform. Break the pieces beside Sam and build another pillar form them. When Frodo gets onto it, push it to the other side. Switch back to him and use the dark cave behind your back to move to the right while avoiding the river of lava. On the other side, hit the stones so that the Hobbits can use the narrow tunnel.
You will have to fight with Gollum once again. In order to defeat him, you will have to keep switching between the Hobbits and throw rock at him. Five accurate throws should let you get inside Mount Doom.
Driven with temptation, Frodo puts the ring onto his finger. Unfortunately Gollum is wary enough to predict where the Hobbits is and jumps onto him. Knock him down from your back (H), switch to Sam (U) and hit him. Gollum will lose some health, but at the same time he will jump onto your character and knock him down to the lower platform.
Build rails from the bricks found here and return up. Repeat the action - this time Gollum will throw you down to a different place, from which you can get back by creating a hook from LEGO bricks, using the rope and building a platform from the pieces on the ground.
Switch back to Frodo, knock Gollum down and hit him with Sam. This time Gollum will throw you down as well - in order to get back, you will need some help. Switch back to Frodo, knock Gollum down and quickly build a platform from the phantom bricks. Now Sam can join the fight and inflict the final blow on Gollum.
Now you have to escape from the volcano eruption and watch the ending cutscene. From now on you will be able to freely explore Middle-Earth, play with whoever you like and collect the missing characters and items.