I love the Lobster Burrito at Lobster Shack!
Great example!
There's seemingly nothing "authentic" about Lobster Shack on the surface. As the sign and decor suggest, lobster rolls are a New England thing! It almost looks like a transplant from the coast of Connecticut. Lobster rolls are not a traditional Mexican dish.
The lobster rolls themselves are really hardly anything like New England lobster rolls, either - they use tail meat exclusively instead of the claw and knuckle typical in New England, even the tail meat tastes pretty different from that of clawed lobsters, the meat is cooked on a griddle with butter, and you can (and should!) get them with cheese and bacon. They make 3 different salsas available. While salsa is immensely popular in New England these days, never with lobster.
Dig deeper, though. The owner is local, and has the very authentic Cuatro Tacos nearby. The lobster is local. This version of lobster rolls is, as far as I know, absolutely unique to Cozumel (and even more specifically to Lobster Shack). Their salsas are unique to them, and their coconut-cilantro salsa is a particularly good match for a lobster roll.
What's authentic about a lobster roll at Lobster Shack? It's that it is a local creation in almost every respect. It honors the idea of a New England lobster roll but ends up being its own unique thing. It's sufficiently different from its inspiration that the two can't be compared in a way that makes either seem to fall short. It stands gloriously on its own as a highly authentic, very local Cozumel lobster roll. It's an honored tradition going back to when Lobster Shack opened not long ago.
This is a superb example of how authentic, local Cozumel food may not match the expectations of visitors.
If it's not clear, I really love the lobster rolls at Lobster Shack about the same as I love the ones at Harraseeket Lunch in Freeport.