An artificial island built on a lake for agricultural purposes is called a

Chinampa. these would be built only on shallow lake beds to prevent flooding and allow the plants to take root, but also so that they may be constantly irrigated. It is almost like a natural form of hydroponic growing in that the water flushes through the plants periodically when the lake rises from rains and falls as to not oversaturate the plants when some of the water drains out of the lake bed.