Hi Myra,
The first bloom photo is a viviparous hardy waterlily bloom, fairly common in hardy lilies with Colonel A.J. Welch in their background. Many yellow and peach hardies have this line and are mildly viviparous in the bloom.
As for Lavender Lace, created by my good friend Rich Sacher in New Orleans, it's a bit of a weed, each pad will create a new plant easily. You will soon be over run with them.
Cheers,
Sean