they do produce seed pods and they will swell and then when the seed is ripe the pods will split open to reveal the quite large seed. you can sow them if you like and get plants for free.

Lilies from seed do take a little patience, though. From seedling to flowering usually takes around three years. Seedlings usually are different from their mother, sometimes in a very good way. You could have your very own variety worth patenting!
If this "fruit" is appearing at the base of the flowering stem, it may actually be what's called a "bulbil"--a tiny bulb that forms on the stem, and is genetically identical to the mother plant. It will take almost as long to bloom as a seedling would.

We regularly collect the bulbils off our lilies and sow them. As TugB says takes about 3 years for them to reach flowering size.