It’s not so much whether Lot knew or didn’t know, it’s that the bible then promotes this story as perfectly OK because it was in the cause of getting to Jesus.
if I got my dad drunk and shagged him and had his baby would you then put it in a book as a shining example of faith and loyalty to your deity? What kind of message is that sending?
You might put it in and say ‘hey kids this is REALLY REALLY wrong. Don’t do this at home. Don’t get your dad drunk and have his baby, because overall its pretty wrong’.
Make no wonder there’s so much bloody child abuse when the ‘good’ book doesn’t even have a bad word to say about dads and their daughters getting down to it.