The three lies will likely relate to all major motivating incidents Anduin has to fight the Horde. The idea Sylvanas was responsible for Varian's death may be one. The reasons for Teldrassil's burning, as you mentioned, may be another.
EDIT: Though technically, saying something like
"For my Father! For the Alliance! For the Light!" could just as easily be three lies, whether Anduin realizes it or not, because the war is truly all for the sake of N'zoth.
Actually, this line of speculation makes me want N'zoth to turn out to be a real character, and actually get a chance to talk to Anduin before the end. Maybe thank him for his service. And considering that N'zoth is the closest standin to Cthulhu, the High Priest of the Old Ones, in WoW, I want to see him using more philosophical and religious phrases. Just to screw with Anduin's head even more, if Anduin's been played.
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And by that, I mean I want N'zoth to show Anduin the Light.
http://www.wowhead.com/news=275764/l...form-is-raptor
Worlds encased in crystalline mountains. Worlds being burned in holy fire. Entire peoples imprisoned and enslaved by so-called "benevolent" tyrants. All to sow the seeds of doubt in the poor boy-king's mind, and for N'zoth to assume the role of a proper psychological villain. To give substance to how the Old Gods can break the minds and spirits of so many, and even shatter the strongest of wills.
N'zoth can show Anduin all the things he's never seen, and ask if he truly wishes to fight for
that. If he still has the same faith. Because who doesn't want to see Anduin's faith tested like so?