@Grf - No, because that's not how production at-scale works.

A "lot" in the pharmaceutical world (and most other process areas where this sort of thing matters -- like paint, for example) is what you produce with one group of ingredients used at one time in a process that can be tracked back to and limited to one group.

So let's say that before you fill the vials you can make 10,000 doses of vaccine from one group of reagents that go at a given time into a reactor vessel and is processed through to the endpoint, which is a machine that fills vials, puts stoppers in them, seals and labels them.

This is one lot. Then the device(s) used to do that are cleaned and the process is run again, and a DIFFERENT lot number is assigned.

You do it this way because if something goes wrong you need to be able to figure out what the scope of the problem might be so you can tell people "GET THAT SHIT OUT OF USE NOW!" and impact only that which you must have destroyed (and thus, in the real world, you have to eat cost-wise.)

For things like paint when you go to buy it ALWAYS MAKE SURE THE PAILS ARE IN THE SAME LOT. Why? Because there are small differences in coloration between them! If you suddenly cut between two lots in the middle of a room there's a decent chance once it dries you'll be able to see it!

If you have a process problem (e.g. the vat wasn't cleaned properly) you now can say "TOSS THIS ONE LOT NUMBER" and the rest are ok. If you have a reagent that went into three lots you can say "toss those three." And so on.

This is why you have lot numbers on pharmaceuticals including OTC, on many food items (grab a can out of your pantry and look; its there with along with the "best by" date), etc. You'll find lot numbers on all manner of things that are not individually serialized but where tracking a potential screw-up without having to recall EVERY item made is important if something is discovered later on.

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