IF THE HEAVILY indebted Latin American countries are to climb out of their hole, they must earn dollars by selling abroad. They can do that only if the industrial countries--above all, the United States--keep their markets open and provide trade financing. Both of those conditions are in doubt, but the immediate threat is a continuing withdrawal of financing by frightened bankers.

Lionel H. Olmer, the undersecretary of commerce for trade, braced the American Bankers Association on that crucial point the other day. The attempts of the Latin debtors to reduce their imports from the United States, while increasing their exports to it, risks increasing protectionist pressures here. It will be essential to withstand them.

But Latin imports from the United States have collapsed to a level that is unsustainable in countries that are rapidly industrializing. If they cannot get at least modest amounts of financing for current trade, the risk of economic paralysis becomes imminent. Yet, as Mr. Olmer observed, many banks are trying to cut back their foreign lending. Others are resorting to complex arrangements requiring collateral, a slow and cumbersome process. As the banks pull back, other commercial lenders--trading companies and exporters--follow their lead.

The process is circular. As Latin economies slow down for lack of imported supplies, the effects are transmitted back into the American economy to the cost of manufacturing industry first and, ultimately, of the bankers themselves. Mexico's imports this year have been about half the low level set by its rigorous austerity program. For American exporters that shortfall has meant some $3 billion in lost sales so far this year--and, as Mr. Olmer observed, that in turn meant nearly a quarter of a million lost jobs for American workers. If the slowdown continues, these countries' chances of managing their debts becomes increasingly remote.

"This red-lining of the private sector in LDCs"-- less developed countries--"is myopic at best, dangerous probably, and may undermine all the efforts that have been made to help these economies adjust," Mr. Olmer said. Having loaned too much and too easily before the crisis last summer, the bankers will not make amends by lending too little now. On the contrary, they threaten to compound the damage.

They have large responsibilities to do their part in keeping trade open in the months ahead, and the Reagan administration is absolutely right to lean on them hard to recognize those responsibilities. "We will look to you to do your part in reestablishing trade financing lines," Mr. Olmer told the bankers, with emphasis. It is the first time that the administration has been so explicit on the subject--a sign of its rising uneasiness about the banks' recent performance.