Best bet. Remove this old drain completely and hire a LMP to burn out the old lead and oakum joint.
Then install a New Cast Iron Inside caulk drain with lead and oakum.
After the joint is properly yarned & caulked then have the plumber use 4 PSF sheet lead as a flashing base reaching about 4″-6″ above grade.
The retaining ring will insure water tight integrity..
.Think about it YOUR spending lots of money and time to install Quality marble just to find out later that the drain or drain connection failed at a later date.
Don’t you think that after 20 years this $45 drain should be replaced?