Why did Lot's daughters seduce their father? According to the Genesis 19:30-38, when Lot escaped out of Zoar, he went up to the mountains and settled in a cave. While in there, his daughters seduced him while he was drunk so that they could bear children and save their family line.

Does this mean saving one's family line is/was so important that you could have sex with your own offspring? Was Lot really drunk to a point that he didn't know what he was doing? Were the daughters wrong to do it? If so, why didn't Lot take any action afterward?
There is no denomination or teaching that I'm aware of that approves of this.  Your question shows a lack of understanding of the basic nature of that the Bible is.

It is not a collection of stories, showing heroes in a positive light.

It is a collection of books including teachings, but also, largely in the Old Testament in the Pentateuch and the Books of History, a book of history.  In a historical book, at least one that is honest and accurate, the failures, frailties, and sins of the people chronicled are not covered up.

Lot's daughters are not the  only ones whose sin is shown.  Adam and Eve eating the apple, David's sin with Bathsheba, Solomon's pride, lust, and disobedience, and hundreds of others.  The Bible includes these sins because they happened, not because they are somehow approved of.  

Far from it, in most of the cases, there are repercussions.  Perhaps not immediate, but they happen.  This is in line with God's nature.  He often gives people the chance to repent of their sins.


  2 Peter 3:9 (KJV)
  
  The Lord is not slack concerning his promise, as some men count
  slackness; but is longsuffering to us-ward, not willing that any
  should perish, but that all should come to repentance.