WASHINGTON (AP) _ The Supreme Court today bolstered the government's power to collect from banks and other lenders back taxes owed by businesses that borrow from those lending institutions.

The court unanimously ruled in a Pennsylvania case that the Internal Revenue Service may sue a lender for back taxes even if the lender was not notified of its tax liability.

Chief Justice William H. Rehnquist, in his opinion for the court, said a notification requirement of federal tax law ''is most logically read not to apply where the government seeks to collect from a lender'' in such circumstances.

The ruling clears the way for government to sue the Jersey Shore State Bank of Jersey Shore, Pa.

The IRS sought to collect back taxes from Pennmount Industries Inc. and said the Jersey Shore bank was liable for approximately $148,600 plus interest in taxes owed by Pennmount for the fourth quarter of 1977 through the first quarter of 1980.

The bank made loans to Pennmount to help meet its payroll. The government sued the bank in 1983, seeking to force it to pay the taxes.

A federal judge threw out the lawsuit because the government failed to notify the bank of its alleged liability within 60 days of the time the IRS decided to assess Pennmount for back taxes.

But a year ago, the 3rd U.S. Circuit Court of Appeals reinstated the suit, agreeing with the Reagan administration that the IRS should not be forced to meet the 60-day deadline for creditors of tax delinquents.

The administration said there are millions of cases each year in which businesses fail to pay all their quarterly withholding taxes due the IRS and that identifying and notifying all creditors of such businesses within 60 days would be an impossible task.

Government lawyers said it also would be a waste of resources since most lenders in such cases are never called upon to pay the back taxes.

The Jersey Shore bank appealed to the Supreme Court to kill the IRS suit.

The case is Jersey Shore State Bank vs. U.S., 85-1736.