When to worry about engine noises?

That’s just not true. All engine oils need zinc. Zinc is part of the dry film lubrication that happens in all engines.

The rings need it. The guides need it. So it has really nothing to do with what lifter you use other than you can use LESS ZDDP with roller lifters and that’s only because the ZDDP is a consumable in the oil. If you start with less, you need to change the oil sooner with flat tappets than rollers because it gets used up faster.

So the amount of ZDDP (in PPM) is based on what lifter you use because it gets used up faster and not because a flat lifter requires more.

Actually zinc oil additives for synthetic is actually ZDTP, Zinc dialkyldithiophosphate, whereas conventional oil Zinc is ZDDP, Zinc Dialkylphophate.

During engine break-in especially in older engines, you should be using a formulated break in oil. There is intended wear necessary to the rings and cylinder walls to ensure proper ring seating. That is why the manufacturers recommend changing that oil after a brief period. With older engines the piston to wall clearances and bearing clearances are much "looser" so to speak, while modern engines have much tighter clearances and smoother cylinder walls at assembly, roller cams and lifters and well atomized fuel injection to ensure that there is less wash on the cylinder walls.

Zinc and molybdenum are often combined. The zinc has a polarity to it which effectively causes it to suspend itself and become a sacrificial element during the high-pressure / heat cycles of valve trains as well as TDC and BTC stokes of the rings and cylinder walls, the zinc is converted to an ash after the high heat event. The modern lubricants use less ZDDP as it tends to damage the catalytic emissions system. The molybdenum compounds provide lubrication in a more traditional sense.

In most discussions regarding ZDDP additives it is related to flat tappet cams and their failure due to improper break in.

just sayin..