I've seen that happen on a tropical water
lily I had in the deck pond one year.

It's called viviparous reproduction.

Some tropical Water Lilies can be increased by viviparous reproduction. This is the development of tiny plants at the point of a leaf where the two lobes connect. Some varieties will produce plants from wilted flowers; however, this is rare. The small, viviparous plantlets develop tiny leaves and some roots, but don't grow vigorously until the parent leaf begins to die. When you see roots growing, remove the new plant and pot them in small containers and treat as a seedling with 2 or 3 inches of water over the soil. Protect them from direct sun and begin feeding applications of fertilizer.

From this webpage
http://www.iamshaman.com/lotus/cultivation.htm

k :-)
http://tinyurl.com/6bguh ~ new pond keeper info
http://tinyurl.com/yp64db ~ slide show of pond