Also check all the fuses on the PPB board for their correct rating. F7 - F9 are for the coils. If these are over fused, they will create problems.

They didn't start using the 520-5021-05 PPB board until Last Action Hero.
LW3 should have this board, the 520-5021-00 with only fuses F1 thru F6.
F5 is the fuse for the 50V coils.
Those are the flippers, knocker, VUK, Ball Launch and the Laser Kick.
Here is the Tech Chart: http://www.pinballrebel.com/pinball/cards/Tech_Charts/Data_East_Lethal_Weapon_3_Tech_Chart.pdf

Also check the SSFB (Solid State Flipper Board) inside the cabinet on the left side.
It may also have some cracked solder joints.