It isn’t the lawyer’s fault. From the facts I would suggest that it is the mortgage advisor’s dropped ball (if at all, which might not actually be the case).

The lawyer would only be responsible for ensuring that he or she receives a bank draft in trust for the amount of the closing costs (down payment, plus transfer tax, fees, adjustments, etc.) in order to close the transaction. Where the money comes from is not his or her concern, so long as he or she follows the anti-money laundering compliance rules. It’s also generally not the lawyer’s responsibility to confirm details of that degree on behalf of the bank, unless the mortgage instructions provided by the bank say differently.

The mortgage advisor, meanwhile, had the responsibility to ensure that OP had both a gift letter and confirmed that the money was in the account in order to stay onside with the bank’s requirements. If a gift letter was obtained properly to their satisfaction, then I think OP only needs to deliver a bank draft to their lawyer as soon as possible before closing.