Lime Of the two major branches of the lime family, the one most widely cultivated in the United States is the Mexican or key lime. Limes originated somewhere in India or South East Asia. Unlike some of the other major fruit citruses, grapefruits or oranges, for example, the lime is a shrubby plant only reaching heights of between 6 1/2 and 13 feet. Branches are slender with sharp spines. Like all other members of the citrus family, limes are evergreens. The elliptically-shaped leaves are dark green on the upper surface, paler underneath and between 2 to 3 inches long with minute teeth. Flowers are white and can be tinged with purple. The fruit, technically berries (hesperidium) are small, between one and two inches in diameter. The peel is quite thin and pale yellow when ripe. The lime is exceptionally cold sensitive and, therefore, not suitable even for areas where other members of the citrus family might survive.