It is my understanding that Enlightened beings are not subjected to karma. Karma is (roughly) created by thought (motivation), action and thought following the action and so, as you can see, every action stems from thought. Negative action stems from selfish thought, which doesn't resonate with Buddhas, and so how can they create negative karma?
The Dalai Lama (as a human being) is subject to the conditions that come with being human (i.e. he will fall ill, have conditions, and his body will eventually fail). He eats meat due to health reasons, but in an exchange with Paul McCartney, I'm sure (though don't quote me!) that he said that he would look into other means after McCartney pointed out the various ways all nutrients from meat can be consumed without the aid of animal products.
It is said that highly attained monks who eat meat can actually bless the animal the meat came from, though I'm not entirely sure/convinced of this, but then again, I don't totally dismiss it either.
Meat eaters usually eat meat from attachment than from anything else. The Dalai Lama, I would think, is not attached to eating meat and so again, this shows the complete lack of negative thought on his part and therefore, no negative karma.
I should add my usual disclaimer that I eat meat and that I don't actually believe there is negative karma caused by meat-eating, outside having an animal killed specifically for one's own consumption, or killing an animal directly. However, I have to stress that I could be wrong and it's entirely my own opinion - nothing concrete.
I hope this gives you a little more understanding. If not, I apologise for the confusion!