hi You have to make a soldered joint between the lead and normally copper pipe which can then be used to join to any other material eg plastic etc.Any older plumber can do this it is a specilized art not much used these days. In UK this type of joint is not allowed on water pipes and a joint known as a LEADLOK is used but I dont think you can get these in large sizes.If the lead is in good codition you may be able to fit a universal plastic waste fitting on it, this has a nut and a compresion rubber ring.hope this helps. Colin.
What you can do is put a lead ring around the lead to the floor and cut it about 1/2″ above the floor and bend lead over , clean it and and take a 2″ brass nipple and clean one end and paste it and solder it to lead, get a 2″ nohub coupling and go from there.
I take it that the basement floor is concrete.My guess is that there is a cast iron hub not far below the concrete that the lead connects to.Might be worth it to chisel away some of the floor to see if there is cast iron and go from it with a new line.You could also use a nipple the same size as the lead and fasten it to the lead line with a fiberglass repair kit that is used to patch fiberglass boats.I have done this more than once with good results.The lead has to be cleaneds does the nipple.I would try to find a cast iron hub first though.Good luck