That sounds like a real stretch. Sounds more to me like Lot wouldn't take his daughters down the mountain to go courtin'.
Why would Lot purposely allow his family line to die out? Consider, if you will, the importance placed on having numerous progeny in all of the stories in Genesis. One of the central motifs of the story of Abraham is the promise God makes to him that his descendants will be as numerous as the stars in the heavens. Note that his inability to have a child by his wife Sarah was his personal source of grief for many years. Children mean everything in that culture. (As they should in our culture too, but that's another thread.)
So why would Lot not want his daughters to marry and have children? And don't tell me it was the "our father is old" stuff. He obviously wasn't too old to do the nasty with his own daughters.