Discussed here. If LF had died as a result of the duel, pretty much all of AGOT doesn’t happen. To quote myself:
“Jon Arryn isn’t murdered, Eddard isn’t made Hand of the King, Bran isn’t thrown out of a tower, etc. Instead, Jon Arryn and Stannis expose Cersei, she and Jaime and the children are likely executed, Robert remarries Margaery Tyrell, and Tywin faces a united Stark/Baratheon/Tully/Tyrell/Arryn force that he can’t possibly beat.”