Lobivia 'Pink Ice' is a well known hybrid cultivar, you can find plenty of pictures in google. The flower is as expected, large and fancy, a strong intense pink. Not sure what the parents are, some expert might know.

Lobivia 'Purple Ice' I've never heard of. There are hundreds of these Lobivia/Echinopsis hybrids about but the fact that I can't find any reference at all to the name suggests it was just made up on the spot, perhaps for a 'Pink Ice' that was a bit darker.