Concretely, a single lot across the group is the one genuine analytical advantage, because everyone's vial is then covered by the same test.
Ordering a single lot for the whole group is the analytical advantage: one independent submission then characterises everyone's material, which spreads the cost of testing across the participants.
Keep a written record: who contributed, what was ordered, which lot arrived, how many vials each person received and when. It resolves disputes and it is the only documentation that will exist.
Write down who paid what and who received what, before it ships.