Hi Jamo and welcome to GoY. Which particular lily are you asking about, there are an awful lot of them :)

Lily seeds will take years to flower. You will have better success to divide the bulbs/tubers every 3-4 years.

True Bathgate

Yes, you can let the lily go to seed, collect them and sow them.I grow a number of different lily species and most have been grown from seed.
Let the seed head on the lily go brown and dry and, when it starts to split open by itself, cut it off and open it up. There will be a lot of material inside the seedhead - far more seeds than you need and a lot of stuff that isn't seed. Select some of the brown, plump seeds and neglect the rest. These should be sown on a pot and the pot kept outdoors in a sheltered postion so that it is kept damp but not too wet. Generally lilies will floer within three of four years from germination, some sooner, some later. If you develop an interest in lillies then you could buy different seeds, just a few each year, then after about four years you will have a new lily coming into flower every year!
Try looking at this RHS site:
http://www.rhslilygroup.org/aboutlilies/page4.html