Generally speaking, any part of a gas operated gun that's directly exposed to the super heated gas entering the gas system should not be lubricated.
There's no lubricant commonly available that can withstand the super hot gas, and what lubricants do is burn into a tar-like sticky substance that causes stoppages from fouled gas system parts.
For that reason, "most" gas operated guns are run with the gas system dry of any lube, and precautions are taken to keep bore solvents out of the system too.
The High Standard owner's manuals were very specific that the gas system should not be lubricated.
One thing you can do to get the system clean and keep it clean is to buy a jar of Slip 2000 Carbon Cutter and possibly a "lead-away" cloth.
The Slip 2000 is a very effective product for removing all carbon from gas system parts. Simply soaking the area in the jar for 15 minutes will remove most all carbon.
The "lead-away" cloth is designed for cleaning carbon and leading off stainless steel revolver cylinders, but also removes carbon by wiping the part.
Here's a site with several High Standard Auto shotgun owner's manuals:
http://stevespages.com/page7b.htm