Hello, Cipsalot! Welcome to the forums!
Try these two approaches:
approach 1:
1.Stand at the left side of the lever.
2.Hold the -RUN- button
3.Press the -ACTION- button to pull the lever
4.Immidiately after that, press and hold the -LEFT- button.
Hopefully Abe will run off the ledge before the slig shoot him.If that doesnt work, try the
approach 2:
1.Stand at the right side of the lever.
2.Press the -ACTION- button to pull the lever
4.Immidiately after that, press the -JUMP- button.
If any one of these work, sorry
An advice: if you are trying to do something a zillion times and it doesnt work, its probably wrong. There is often more than one solution to every puzzle in the game. Keep trying, and practice your fast fingers