Replace lead pipe with pvc question

I am helping my daughter remodel her bathroom. We are down to the last steps of installing a new vanity, but have a problem with the drain. Her house is ~50 years old and the vanity drain has a lead drain pipe with a chrome drain pipe leaded or soldered which has partially rusted through. There is only about 1 1/2" left to connect the p-trap to under the sink. In the wall (vanity not yet installed), there is a cast iron drain (2" I think) with a lead pipe connection leading to the wall (see picture). My question is, can I remove this lead pipe connection and replace with a neoprene or similar type of connector to PVC and then connect the sink drain to the PVC. It looks like there is enough of the cast iron pipe sticking out of the hub for the connection if I do not damage it. I am concerned that the chrome drain pipe will continue to rust and will have to be repaired sometime in the future, and would like to put in a more permanent fix at this time. The connection looks like something was wrapped around the pipes to seal the connection but I am not sure. Would this also have lead connecting it? Thanks for your advice.

The lead joint would NOT have bonded to a cast iron stub, so it SHOULD be a brass wiping ferrule and if so it is tapered which makes clamping to it problematical.