[Eurytus]

I think that the fact that Tolkien wanted to show the war as being one of the whole of Middle Earth was certainly a reason behind Sauron attacking Lorien and the Lonely Mountain. But given that this information is hidden away in the appendix we must assume that this reason was a minor one. I think the main reason that Sauron was fighting on three fronts was simply because he was totally undefeatable in military combat. He had more armies than he knew what to do with. He certainly had enough armies inside Mordor (held in reserve) to more than deal with Gondor and therefore probably did not consider it a problem using his forces in Mirkwood to attack Lorien and those from Rhun to attack the Lonely Mountain.
From his point of view the West could not win and therefore even though the army committed to attacking Lorien was not strong enough to succeed, Sauron would have been able to crush them after defeating Gondor.
A possible lesser reason for attacking Lorien might have been to prevent the ring from travelling there. We can assume that Sauron believed at first that Saruman had the ring, subsequent to that he may have believed that Aragorn had come into its possession. That may have been a bad scenario for Sauron but he would have been comforted by the fact that Men had proved highly corruptible in the past. After Numenor and Isildur Sauron certainly would not have been too concerned about Aragorn destroying the ring and would have been fairly confident that he could defeat Aragorn even though the latter had the Ring. After all Sauron was still the rings master.
However he would have been greatly concerned had Gandalf claimed the ring, since he would have been strong enough to possible defeat Sauron with it. Apart from Gandalf perhaps the only other person who would have been capable of mastering it would have been Galadriel, whose true strength is only really revealed in the Silmarillion. Sauron would have been rightly concerned had the ring found its way to her. So the attack on Lorien could have also been for the purpose of preventing the ring from making its way there.

One thing that would suggest that the Nazgul would not lead any attacks on Lorien is this. As mentioned previously the Nazgul’s primary weapon is fear and it seems like those who have dwelt in the undying lands are somewhat immune to this. Witness Glorfindel for instance. I think it is certainly true to say that the Nazgul would be far less effective against Noldor than against men.