How to support a heavy wooden lid in a copper sink
I would create some hooks out of straps of metal to hold the lid in place.  If you made these out of copper, they would match the sink.  You could probably make them out of plumbing pipe, which you sand, hammer flat, and lacquer.  Alternatively, stainless steel to contrast with the sink.

You'll need to think about a handle so that you can get the lid in and out.

Section view:

 ----+              +----
\\\##|\\\\\\\\\\\\\\|##\\\
   ##+---         --+##
   ##                ##
   ####################

# - Copper sink
\ - Wooden worktop and lid
- - Metal hooks


Plan view

\\\\\\\\\\\\\\\\\\\\\\\\\\
\\\\\\\##############\\\\\
\\\\\\\#\\\\\\\\\\\\#\\\\\
\\\\----+\\\\\\\\\\+----\\
\\\\\\\#\\\\\\\\\\\\#\\\\\
\\\\\\\#\\\\\\\\\\\\#\\\\\
\\\\----+\\\\\\\\\\+----\\
\\\\\\\#\\\\\\\\\\\\#\\\\\
\\\\\\\##############\\\\\