Why?
Lynn has been a finalist for numerous HC jobs the last couple years (Dolphins, Jets, 49ers), and is a favorite of the Owners Terry and Kim Pegula. They basically forced the move mid-season to fire Greg Roman and make Lynn Offensive Coord.
Since the offense responded quite positively to Lynn's approach (not to mention the running game has been #1 the last 2 years and he is RB coach too) he is the one coach considered too important to the Bills to lose.