Drains are not made of lead that I ever heard of.  The cast iron ones do have lead to hold the connections together from the outside of the pipe.  Water mains, yes, they have lead in the pipe.

Now, the sink clog.  The plumber's been out once, and probably snaked the drain.  That's probably what you need to do again.  It's cheaper to buy a hand snake for $10 or $15 and do it yourself.

The real problem is that it is happening so soon.  This might indicate a physical problem with the pipe, but in most cases I would say it's something that you are putting in the garbage disposal or sink drain that doesn't belong there.  Celery, bananas, hair, chitterlings and other stringy items can clog up a drain really fast.