Why do elves eat?

correct me if I'm wrong, but isn't it true that elves only can die from three things (battle,grief or getting tired of the world and leaving their bodily attachment to the it). So why do they eat lembas and stuff? perhaps they can survive without food but they will look like gollum after a millenia of two? =)

maybe there's a simple answer to this but I'm to lazy to seach it up.