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
Speaking of Precision Blog 
[…] do is make the steel any softer or easier to deform. For a better description see this site: Why Lead Is NOT An Alloying Element In Steel | Speaking of Precision Blog So unless someone is buying steel with lead mixed in and making the rivets on a lathe, I doubt any […]
I feel the need to point out that machinability is a property which lead changes. Saying lead isn’t an alloying element because it forms a separate phase is like saying copper isn’t an alloying element in aluminum because it can form incoherent precipitates. Different phase /= Not an alloying element. Plenty of additives aren’t soluble at room temperature.