i was on the Lukla-Mera-Lukla trek on April 2005, and, even if our western guide was vegetarian (and she didn't like eggs, as well) , we had no problem at all (see the 5800m lunch picture!), but the point was that everything was organized in advance by our trekking company (also dietary requirements)
in any case in the hinku vally there are teahouses in which i saw eggs and vegetables, but i do not know how much of them was available for sell
i think the best option is to arrange in advance with the sherpa guide