On my old browning citori - when I bought the gun, I removed the iron and coated the forearm wood to waterproof it. At that time, I cleaned the iron parts and reassembled the gun. That was in 2000. fast forward to now, and I removed the iron to fit it to a new stock. One of the ejector hammer springs was actually fractured but the ejector was still working fine!! But I should complete the stock work this week and then I will just reassemble the forearm iron with new ejector hammer springs. the only lubing I ever did or will do on that assembly is grease the latch (clean off old first and then apply a bit of new). always remember that lubricants attract dirt and lubricants don't get along with wood very well. So if you are going to start lubing that assembly, you will be stuck tearing it down and cleaning it up regularly. That process is going to put some miles on those screws that you don't want. This part of the gun was not made to take apart on a regular basis.
PS - I have registered more than 25,000 doubles with this gun + lots of practice + this used to be my only trap gun and I shot all the games with it - registered, practice, meatshoots, and winter league.
Like Gary, I have sealed all of the unfinished areas of my forearm with a sander/sealer. I clean the forearm iron like I clean the rest of the gun. Dip a small paint brush in the cleaner and brush. I do this over a catch can. Then dry out the cleaned area with a rag. It costs me about $10 to make a gallon of cleaner and I am not stingy while using it.
There are three areas in the forearm of my gun that should be lubed every time (ejector hammers and sears/forearm latch). I use Gator tears but any good lube will work.