They're not seeds, they're called bulbils. Basically they are mini lily bulbs....good thing too because most lilium lancifolium are sterile. If you don't already have them in your area, a word of caution....Tiger lilies are also a favourite of the bright red lily beetle.

Yes, that's a Lilium Lancifolium... tiger lily. I think they're fabulous. They do come in other colors - yellow, cream, lavender, pink. I actually found a package of mixed at KMart years ago, but the other colors have all either petered out or reverted to orange. You might find them at some real specialty bulb mail order company. I've simply learned to love the orange.

Very easy to grow - the bulbils just fall naturally, dig themselves in and sprout around the parent plant. The first year growth is a single shiny lanceolate leaf (could be mistaken for a grass or a weed and pulled up or dug over). The second year is a spindly plant that looks like the parent. They reach blooming size in three or four seasons.

I'm surprised you didn't get anything - the germination rate seems to be about 100%, if my yard is any indication. If you've got bulbils from your plants now - don't save them in a bag, scatter them now since this is the time they're dropping and seeding on their own. Sunny location marked so you know where they are. And no need to push them more than barely, if that, into the soil - the little white root foot pulls them down. You can also put some in a pot and leave outside for a couple of seasons until they can be transplanted easily.

We don't get the red lily beetle. I've also read it's best not to plant tiger lilies with other lilies because they can be some kind of disease carrier that could infect fancy Orientals, etc.

If you want to move the ones you have, let the stalks and leaves turn brown. Cut the stalk down just to make it easy on yourself and dig deep since you'd be surprised how far down they've pulled. Judging by the size of the plant in your picture, the bulb should be fairly large. Replant 6" down in any sunny location.

Actually, the other colours are just hybrids with other Asiatic species, not 'pure'lancifolium (tigrinum) . There is a natural diploid form var. flavum , which is yellow and fertile. Another form is var. fortunei, which is bigger in all aspects and slightly different shade of orange.
The bulbils need vernalization to grow and flower. You can cheat them by putting them into a refrigerator for some weeks. If the autumn is long and warm they can make some growth.

No need to refrigerate the bulbils in Wisconsin (I think the OP is in Wisconsin) or where I am in Minnesota - our often early autumns and long winter seasons take care of that without doing any additional cold storage. Been growing them here for years simply by dropping them where wanted once I notice they're naturally falling from the parent plant.

I was not talking about additional cold storage.Please reread what I wrote. You can collect bulbils early and put them in the fridge for 4-6 weeks. Then if the autumn is long(nobody can guarantee, I know) you can make 1 season of growth the same year(if you're in a hurry), especially if you have a green house. Just like with seeds of many lily species. There is nothing additional about it, it is just a way of saving 1 year time