Rex is not a lame duck. He has two years. That is stable enough by NFL standards. There is no reason to extend him with two years left on his deal.
Coughlin was never a lame duck with the Giants. He never entered a season on the final year of his deal. The Giants extended him right before the 2011 season just to avoid that. I have heard Mara speak many times on this subject. He does not like lame duck HCs. The Giants prefer to extend of fire their coach before the final year of their contracts. After the Giants won the SB, Coughlin was extended prior to the 2012 season.
They did the exact same thing with him prior to the 2007 season.