Lilium Tigrinum (Tiger lily). Yes, if you take the little bulbils and plant them, you will get new lilies. The success rate with this lily is very high. It will, however, take at least three growing seasons to reach blooming size.

The first year, the sprouts will look like a shiny lanceolate blade of grass - good idea to plant them somewhere where you can identify them easily and not accidentally dig them up or plant over them. The second year they will look like a spindly lily stalk.

I have many stands of them scattered around my gardens - I think they're delightful; one of the few true lilies that is completely no care.