If it is a cash deal, there should be no time involved in getting a clear title.
As stated, meet at YOUR lender, give them the cash, they give you a lien release which you give to the buyer along with the Bill Of Sale. The lender gives you the title, which you sign over to the buyer, the lender's Notary notarizes your signature(s) on the title, and it is a done deal.
If any kind of a check or money order is involved, THEN it gets interesting. the lender probably will not release the lien until the check is verified and cleared.
The bottom line is, YOU must contact your lender and see how the transaction must be done to keep them happy. If the lender is not happy, the buyer and seller will not be either.