cleaning the chain

This chain is made about 30 years ago.
When I made my python, I bought 2 donor bikes which were made in about 1980.
Before making my python, I cleaned it. Now almost 2 months have passed.

 The chain's color is black. originally it's silver. very dirty.

I cleaned it with the gasoline. we can see some silver parts.
Off course I cleaned chain wheel and rear sprocket.
Finally I attached the chain to bike and gave the lub.
Is the cleaning  needed once a month ?
If non oil chain is used, we don't have to any lub for it ?