Unlike the U.S. M1 and M14 rifles, no grease is specified for the FAL, only oil. There doesn't seem to be any magic oil; they all pretty much work the same. CLP is as good as any.
I have not noticed a greater need for oil on the FAL than the AR. Your FAL might need a bit of tweaking.
Aside: Despite the FN recommendation, I have been known to use both grease and oil on my FALs with no apparent ill effect. Follow the same guidelines as the M1 Rifle: if it slides, grease it; if it rotates, oil it.
From the FN Manual:
The L. A. R. functions with very little or practically no lubrication.
Before firing, wipe off any oil remaining on barrel and gas cylinder surfaces; if the piston and chromed part of the gas plug have been slightly oiled, dry clean these too.
The tabulation given below gives on one side the list of parts which can be slightly oiled, on the other the list of parts which require no oiling and which, in some cases, can be adversely affected, if oiled.
OILED
- Inside breech block slide (the bolt carrier).
- Breech block, at locking shoulders.
- Body (bolt), at bottom and along guide grooves for slide (bolt carrier).
- Holding open device.
LEFT DRY
- Barrel.
- Gas cylinder.
- Piston, if chromed
- Gas Plug and ports
- Outer surface of slide (bolt carrier)
- Front face of breech block
- Magazine and platform (follower)
- Magazine catch
- Sights