Can my lawyer refuse to close if the other side's paperwork isn't ready even though the money is?

Yes, and this is generally what your lawyer should do. Having the money ready is only part of what makes a closing complete; your lawyer also needs the actual registerable documents, discharges, and any other paperwork required to properly transfer and register title, and releasing funds before those are in order can leave you exposed even if the cash side looks fine.

If the other side's documents are not ready, your lawyer may propose alternatives rather than an outright stalemate, such as a short delay, a solicitor's undertaking from the other lawyer to provide the missing item shortly afterward, or a gap closing that lets the practical parts of the deal proceed while the paperwork catches up. Which option makes sense depends on exactly what is missing and how confident your lawyer is that it will actually arrive. What your lawyer should not do is release your funds or complete the deal on faith that missing paperwork will show up eventually, since that shifts real risk onto you without your full understanding of what is happening.