What happens if the seller's lawyer never actually delivered a document I was promised at closing?

If a lawyer gave a professional undertaking to deliver a specific document after closing, that's treated as a serious professional commitment, not just an informal promise — undertakings between lawyers are taken very seriously and are subject to the profession's own oversight, separate and apart from whatever the seller's own contractual obligations happen to be under the purchase agreement.

A buyer facing a broken undertaking should start by having their own lawyer follow up directly and formally with the lawyer who gave it, since this is how most situations like this actually get resolved. If that doesn't produce the missing document, further avenues exist, including raising the unfulfilled undertaking with the Law Society, and, separately, pursuing the seller's own contractual liability if the missing item was also a closing requirement under the purchase agreement itself, not just something a lawyer personally promised. Keep a clear written record of exactly what was undertaken and when, since that record is what makes any follow-up effective.