I'm not a fan of the burritos at Lobster Shack. All that rice drowns the other ingredients. I am quite fond of their lobster rolls. They're not much like a New England one, but they don't need to be. Avocado goes really well with lobster, and they grill their lobster meat with cheese which is pretty darned tasty as well.
I've had the lobster bacon sandwich at Le Chef several times. It's usually pretty good, but if I get lobster in Cozumel it's much more likely to be a lobster roll from Lobster Shack.
Well that is on my list too, but La Chef had seniority for a try. What non-lobster or fish stuff does the Shack have. (I know, I know, but I have to keep her happy....)