Though today people use refined vegetable oil as fat for cooking, the ancient Mexicans used lard. Butter is never used in a traditional Mexican cuisine. Lard adds aroma and favor to the masa used for making tamales.
Authentic Mexican Recipes Cooked With Lard
It may surprise some but lard is used all the time when cooking authentic Mexican recipes. Butter is used in the Mexico a lot, but as Mexican cuisine author Maya Pillai plainly explains, if you're eating butter, you aren't eating authentic Mexican:
Read her interesting article about some of the history of Mexican cuisine.