Lead is added to steels to improve their machinability. But Lead is not considered an alloying element.

An Alloying element is “An element which is added to a metal (and which remains within the metal) to effect changes in properties,” according to my copy of the Metals Handbook Desk Edition.

  
Arrows point to lead.

While lead is an element that is added to a metal:

  • It does not remain in the metal, it remains separate from and mechanically dispersed in the steel  as ‘inclusions’ when it solidifies. It is the dark material on the ends of the manganese sulfides in the photo above.
  • It does not change mechanical properties of the steel.

“Lead can be added to both carbon and alloy steels to improve machinability…The lead is present as small inclusions that are usually associated with the manganese sulfide inclusions…Lead has no apparent effect on the yield strength, tensile strength, reduction of area, elongation, impact strength, or fatigue strength of steel. “- Cold Finished Steel Bar Handbook
For this reason, the addition to lead to steel is not considered an alloying addition. The addition of lead is a great way to improve the economics of machining and improving the surface finish of  complex parts from steel.
Photo from L.E. Samuels Optical Microscopy of Carbon Steels