If the lender will not voluntarily provide their SSN, I have two recommendations:

1. Send the lender a polite request for their SSN, explaining that you are required to report it on your tax return because you are claiming a mortgage interest deduction for what you have paid to them. Get proof of mailing and receipt.

2. Give them a little time (10 days ?) to respond. If they don't, print the return to file by mail without the lender's SSN. Include a brief letter to the IRS explaining your efforts to obtain the SSN of the lender and that you have records of all payments.