The Regal lily (Lilium regale) has definite apomictic tendencies. It often produces seeds that are exact, identical copies of itself, regardless of whether flowers are pollinated or not. So yes, you should get seeds as the man says, but you're not required to pollinate from different flowers on the same plant. And yes, the regal lily is one of the best for beginners wanting to grow from seed.
On another note, the theory that pollination (for any flower) might work better if you cross pollinate different flowers on the same plant, versus the same flower pollinating itself, is a wives' tale. Success (or failure) will be the same in both scenarios.
Certain other lilies can also produce apomictic seeds, but not as sure fire as L. regale. The Formosa lily and Philippine Lily (Lilium formosanum, L. philippinense) are self fertile, and will produce seed if flowers are pollinated by its own pollen (or others). These are easy lilies from seed also, and easy to produce your own seed from them.
