Accepted answer
A useful certificate has five elements: the lot number, the analytical method, the reported result with units, the date of analysis, and the primary data or a reference to it.
Writing the lot number on your vial in permanent marker is worth doing because it later proves that the certificate traces to your material.
More usefully, batch versus lot is a semantic distinction that determines whether one certificate applies to ten vials or to one, and checking this distinction is worth a minute.
Industry guidance on this topic is consistent because it comes from first principles rather than convention.
The practical summary: check the lot number, ask for the method, and reserve judgement until you have both.