SU carburetors need oil in the dampers for proper operation of the dashpots on top. the damper works as a shock absorber to slow down sudden rise of the air piston for fuel mixture enrichment on acceleration. Originally prescribed oil was "Lucas Carburetor Damper Oil", which is essentially 20-weight hydraulic oil. Thicker viscosity oil will slow the motion a bit more, giving a bit more fuel enrichment on acceleration. You may hear recommendations ranging from 10W to 90W, But almost any kind of oil will work. Commonly just use whatever oil you use in the engine.

Correct oil level in the damper will be below top of the smaller inside tube. As long as the brass piston is submerged in oil it will work. You can determine this without even looking. Unscrew the damper cap, lift it up and press it down with one finger. If you feel resistance to downward motion before the cap hits the threads, that is enough oil inside.

Instruction from the Operation Manual (Driver's Handbook):
CARBURETOR DAMPER
Every 1000 miles (1600km.) unscrew the oil cap at the top of each suction chamber, pour in a small quantity of thin engine oil and replace the caps. Under no circumstances should a heavy-bodied lubricant be used.
Failure to lubricate the piston dampers will cause the pisons to flutter and reduce acceleration.
An oil indicated under Ref. D/F should be used.
Oil Can and Carburetor:
Motor oil 20, 20W, 20/20W, 20/30W