In the most recent update, Turbine made all of the Volume II quests soloable. That should not be taken to mean that they are easy. Unless you are capable of taking down a raid mob with 18,000 morale using only your skirmish soldier for help, you will not be able to get through all of them. In fact I died four or five times learning how to kite effectively on my hunter the first time I encountered one of those monsters. I didn't mind though, my solo game has definitely been kicked up a notch by the experience. More than any other MMO I've played, modern LoTRO seems to have nailed the "challenging but fair and rewarding" solo play experience.
Volume II tells several really interesting stories that fill out Tolkien's original work in believable ways. In my mind they expand the lore rather than clash with it. Volume I was interesting, but it felt like more of a side story that was only vaguely connected to the books. Volume II is more directly connected to the books, it deals with the aftermath of the fellowship passing through Moria and Lothlorian.
The first part of it tells the story of how the dwarves recolonized Moria. This may seem like a bit of a stretch at first, because as near as I can remember Tolkien never mentions this happening. However we do know from the books and extended material such as Lost Tales that there would have been a power vacuum after the fellowship passed through. Obviously the biggest bad down there was the Balrog, which Gandalf took out. However the fellowship also took out a lot of the leaders of the orcs on their way through. The orcs of Moria even sent a large hunting party after the fellowship to try and avenge the deaths of their leaders. So there would have been opportunity for the dwarves to retake the halls.
Further, the dwarves would almost certainly have wanted to retake Moria if it was possible. If you reread "Durin's Folk" in Appendix A of The Return of the King, you can get an idea for what it represents to many of the dwarves. It almost directly sets up the first part of Volume II. In one part, the dwarves fight a long and bloody battle for revenge that ends on the steps of Moria. At the end of the battle, the heir of Durin (Thrain) wants to go in and retake the halls. However the dwarves from other clans that are with him refuse. The one dwarf that nearly entered Moria during the battle (Dain) says this to him, after returning from the gate ashen faced with fear:
"You are the father of our Folk, and we have bled for you, and will again. But we will not enter Kazad-dum. You will not enter Kazad-dum. Only I have looked through the shadow of the gate. Beyond the gate it waits for you still: Durin's Bane [the Balrog]. The world must change and some other power than ours must come before Durin's folk will again walk in Moria."
So we are left with a very strong impression that they would like to retake Moria, save that they have no hope of facing the Balrog.
The next part of the Volume deals with what the elves of Lothlorian were doing after the fellowship passed through. This conflicts a little with the Appendices, which imply that the elves were holed up in Lothlorian until after Sauron was defeated:
"After the fall of the Dark Tower and the passing of Sauron, the Shadow was lifted from the hearts of all that opposed him... Three times Lorien had been assailed from Dol Guldur... Though grievous harm was done to the fair woods on the borders, the assaults were driven back; and when the Shadow passed Celeborn came forth and led the host of Lorien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed."
Turbine gets out of this quandary by casting the battles in Dol Gurldur in Volume II as a feint to distract Sauron from the fellowship, and implies that it is this first assault by the elves on Dol Guldur that precipitate the attacks by orcs on Lothlorian during the rest of the timeline of the books. You can read the end of the quest here, obviously a GIANT SPOILER if you haven't finished Volume II.
As a bonus, one of the quests in Volume II deals with events that occurred just before the Hobbit. Only a short reference is made to it in the Appendices, but you can find a more detailed account of them in either Unfinished Tales or Lost Tales (I get them mixed up). An evil power known only as "the Necromancer" has been holed up in Dol Guldur for some time. Gandalf begins to suspect the Necromancer is more then he seems to be, goes to investigate, and finds some surprises. The quest actually expands on this part of Tolkien' s work in logical way, answering burning questions such as: [SPOILER] "How the heck was Gandalf able to sneak into the middle of an enemy stronghold inhabited by Sauron?"[END SPOLIER]
My only real criticism of Volume II is that mechanically, due to crazed travel times, there were some quest chains that would have been quite painful were I not a hunter or warden. Even as a hunter with all the stables unlocked and the ability to teleport willy nilly all over middle earth, there were a few nights I spent more time riding my goat around in Moria than doing anything else. It wasn't as bad as Volume I in this respect, but it could still use some improvement.
However, all in all I was really pleased with Volume II; particularly with the stories it tells. While it's pretty much Lord of the Rings: Expanded Universe material, I think overall Turbine did a great job with it. Now that the book quests are soloable, it feels almost like there is fun story driven single player RPG embedded in a full featured MMO. I definitely give Volume II the thumbs up, and I'm really looking forward to Volume III.