Is it permissible to lie to one person to help another pay off a debt, such as the creditor claiming to be the original debtor to avert harm from his debtor?

Lying is forbidden, and its prohibition increases if it involves deceit, fraud, and taking others' money. What you are asking about results in money being paid to you based on the premise that you are the borrower, which is contrary to reality, so it is not permissible. This action does not justify warding off harm from the debtor.

Sheikh Ibn Uthaymeen was asked about a person who took zakat money from a friend to distribute it to the poor, but he himself was in need, so he took it for himself and paid off his debt without the owner's knowledge, telling him that he had distributed it. He replied that this action was a grave mistake due to his lie to his friend. The proper course of action for him would have been to seek permission before disposing of it. If permission was granted, there would be no harm. Otherwise, he must return to the owner, inform him of what he did, and seek his forgiveness. If the owner permits it, the owner's liability for his zakat is absolved, and the taker is free from sin. If he does not permit it, the amount must be returned to its owner so that he may pay the zakat himself.