The House voted last night to let President Carter determine when to lift economic sanctions against Zimbabwe-Rhodesia.

By 350 to 37, the House adopted what was labeled a compromise position between those who wanted to lift sanctions immediately and those who wanted no action taken at all.

The bill worked out in the House Foreign Affairs Committee would lift sanctions by Oct. 15 unless the president determine that it is not in the national interest to do so.

Passage of the bill was victory for the White House and gives the administration a chance to soften the Senate position by negotiating new language during a House-senate conference. The Senate recently voted 52 to 41 in favor of requiring the president to lift sanctions immediately. If similar action had been taken by the House, the president almost certainly would have vetoed the legislation.

Action on the controversial foreign policy issue was the last major task the House was expected to undertake before adjourning today for a 10-day July 4 recess.

The House defeated 242 to 147 efforts by conservatives to adopt an amendment that would force the president to lift sanctions by Dec. 1, unless Congress passed legislation continuing the sanctions.

They argued that sanctions should be lifted by that date because a black majority government was elected in Zimbabwe-Rhodesia last April, achieving the goal of black majority rule through free and fair elections.

The government of black Prime Minister Bishop Abel Muzorewa needs the encouragement of lifting sanctions to make further progress toward democracy and to help his people, according to the House conservatives.

"Either thiss country believes in the ballot box or it doesn't," Rep. Henry Hyde (R-III.) said.

"They need food, they need trade. They don't need words on paper," Rep. Robert Bauman (R-Md.) said. If the Muzorewa government falls, "we will have another black African nation under Marxist control," he said.

But Rep. Stephen Solarz (D-N.Y.) argued there was no need for this country to be the first to lift sanctions and take the lead when the British, the former colonial power in Rhodesia, have not yet decided to do so. Solarz said lifting sanctions would remove pressure on the Patriotic Front and The Salisbury government to end the war, and eliminate the need for further democratic concessions to the black majority.

Lifting sanctions now would be "a diplomatic disaster," Solarz said, because the United States would lose support among other black African nations and provide the Soviet Union with a "golden opportunity" to make further inroads in black Africa.

Nigeria has threatened to cut off oil to the United States if it lifts sanctions now, but Majority Leader Jim Wright (D-Tex.) argued that Nigeria's position should not be taken into account if lifting sanctions were the right thing to do. Republican conservatives, however, called Nigeria's threat "blackmail."

In 1968, the United Nations Security Council prohibited all trade with Rhodesia to protest its racial policy and to bring pressure for majority rule. The United States exempted itself from the sanctions in trade on chrome and nickel until 1977.

Last year the Case-Javits amendment adopted by Congress said sanctions should be lifted if Rhodesia held an all-party conference, followed by free and fair elections.