Anthony Ruh wrote an answer about La Sportiva Glacier WLF Mountaineering Boot - Men's on February 12, 2012
I did the same trek last September/October in light hiking boots (Merrel Moab Ventilator Mid), carrying a 35 lb pack. My buddy did the same, and I saw a couple with the same shoes. Very doable. Those would be similar to La Sportiva's FC Eco 4 or the Thunder II. Of course, there are also tour groups full of people with mountaineering boots too.
It comes down to how comfortable you want to be and how much you want to spend. As long as it's a mid height boot you probably can't go wrong.
It's just a vigorous hike. And the Sherpas often wear Crocs or Chinese sneakers.