We know that LW was not killed on the orders of Manderly or Mance/Abel for sure...people think that BW killed LW, but I beg to differ.
BW's motive
Goes ahead in line of succession to the Twins
Reasons for this motive's failure
There are simply too many Freys ahead
LW was stronger and bigger in size, so no way BW could've overpowered LW and killed him.
BW thought that neither of them would never inherit the Twins in ACOK.
LW was the cruel one, not BW..