I don't think this is anything we can really answer. It depends on the nomenclature that your supplier uses. We have steel suppliers that use heat numbers and some that refer to a lot number.
You need to ask. It may be that there was secondary processing (such as HT) that was only done on part of the heat so it gets a lot or batch number.
But this other number should be in addition to the heat number.
And then there are translation issues.
Ask.
Isn't the point to provide an index into the supplier's QA records and to identify anything with identical processing in the case a problem is identified? For both of those the only requirement is the numbers represent that commonality and offer that traceability. If that's not understood as a requirement before the order is placed and a review of the supplier record system to validate their QA, most of the leverage that existed when placing the order is gone now.
Even consecutive numbers won't help much - it's possible to screw things up on just one group of material.
so a lot # can be a lot of parts manufactured , a heat lot# is the heat # from the mill or from heat treating, then there a serialized, same heat lot # and all parts are the same lot# during manufacture.