Only some species daylilies can be invasive, not the hybrids. I have about 100 daylilies, not one of them is invasive.
Lilies like well drained soil, full sun. Many of mine are in large pots on my deck and patio, when they are done blooming, they get moved off the patio.
Here is the database for liliums, lots of lovely photos
http://garden.org/plants/brows...