"Stargazer" is an Oriental lily, not an Asiatic. The link below gives you a very basic introduction to the difference between the two types. The internet is just filled with more detailed info.

Here, in a lower zone, I plant lily bulbs in the fall - late September through October while the ground is still workable. Even though I have ideal conditions for all types of lilies, I've found that Orientals do great in year one, less so in year two and then just disappear altogether by the third year. Others have different and better experiences with them. Asiatics, on the other hand thrive for me and get better every year, producing more bulbs and stems and expanding the clumps.

Here is a link that might be useful: Lilies

I mainly plant lilies in the fall and early spring. Once in a while, I transplant them in late summer too if I happen to get them.

I gave up on Orientals because they are not long lived in my garden as duluthinbllom stated. I only have Asiatics, trumpets, orienpets, Lilium longifolium, and Lilium speciosum in my garden now. The Trumpets and Orientpets satisfy my crave for fragrant lilies.