...and just to throw this in....new cars have roller tappet cams so no need for Zddp in them.
I've built several engines and, as suggested above, put a quart of the EOS (engine oil supplement) from the local chevy dealer and have never had a problem running conventional oil later which has always been Castrol and Valvoline.
Just finished putting a new cam in a 77 Firebird and did buy the bottle of ZDDP additive this go round. All is well.
One of the main things to remember, even with ZDDP, is to get the engine running ASAP to avoid the engine "grinding" over a lot before it starts...to be on the safe side.