The most reasonable way I think of it is we are not working with lilies that occur naturally due to the human intervention (wide crosses and embryo rescues). Hence there is no biological sensibility in that they can not have evolved to adapt to our meddling with their genetics.
As for Tiger Babies x Landini I would not expect that to work. If Tiger Babies is indeed triploid you want to go higher in chromosome count for your pollen parent (Landini = diploid). At least that is what I read somewhere, probably yahoo lilium group (sign up if you haven't already).
Don't worry, it was a long road for me to come to the understandings that I have now. I remember when I couldn't tell the difference between Asiatics and Orientals.