Yes, the scientific name (genus) for a true Lily is Lilium. I've never heard of Aster Geizer. Maybe, 'Stargazer'? If so, it is a very common Oriental Lily. I would not pay more than $2 per bulb for it. It is widely available in garden centers and big box stores.
You can find tons of info about Lily culture on the North American Lily Society web site.

If the beautiful lily was deep pink with white edges, it was "A Star Gazer"--and it was criminally overpriced.

By now you have used Google to find out all you will need to know about growing them---you can order them and many other lilies from such vendors as Scheepers & Brent & Becky's. Visit the Garden Watchdog website to read consumer ratings of companies they have ordered from.