I've had some Indian friends (i.e., jains, hindus, buddhists, muslims, etc.) who are vegetarians (of some sort or another or don't eat meat under general circumstances) visit Argentina and they could eat some good pasta, salad, and some other dishes that met their needs all around town, including at the steakhouses that I love. [The selection is limited, but there'll be no need to starve either.]

If the need goes to a dedicated vegetarian-only kitchen (and particularly one that doesn't even use eggs and/or milk in some cases), then things become more difficult and what we found to work out well was to get a short-term apartment rental where they could make their own food. Grocery shopping in other countries can be an experience in and of itself.