Armed with disputed testimonials that last month's parliamentary elections in Rhodesia were conducted freely and fairly, conservatives who have been chipping away at the Carter administration's Rhodesia policy for nearly a year begin what they think is the final assault this week in the Senate.

A flurry of fact-finding reports and lobbying by American citizens who either observed or analyzed the conditions of the parliamentary elections has set the stage for the battle, which begins on Tuesday when Sen. Jesse Helms (R-N.C.) introduces legislation to overturn economic sanctions against Rhodesia.

Helms and other conservatives want to restore U.S. trade with Salisbury as encouragement for the government being formed by Bishop Abel [LINE ILLEGIBLE] led by former minister Tan Smith.

Paradoxically their effort is being bolstered by the active lobbying for a more sympathetic U.S. position to ward the Muzorewa Smith government being done by two self-asserted liberals Bayard Rustin and [WORD ILLEGIBLE] Lowenstein.

Rustin, the black civil rights leader who heads the A. Philip Randolph Institute, and Lowenstein, who played a key role in the liberal drive in 1968 to dump Lyndon B. Johnson, were part of a nine-member delegation of observers. The group formally reported Thursday that the elections "in spite of serious imperfections" were "a relatively free expression of national will [and] a significant advance toward multiracial rule."

Lowenstein's aggressive plunge into the racial conflicts of Southern Africa in recent months has stirred ripples of curiosity across Washington. He has lobbied by his own count about 100 senators and representatives as well as top officials in the Carter administration to reconsider the firm U.S. opposition to the "internal settlement" designed by Smith.

And Rustin's involvement has drawn him rare sharp public criticism from other black leaders, who appear to form a united front of opposition to any change in Rhodesia policy.

Helms' supporters claim they count 53 votes for lifting sanctions now. They argue that the government-estimated 64 percent turnout in national voting for 72 black parliamentarians last month was "free and fair" particularly by the standards of the black African nations the Carter administration has sought to woo diplomatically.

The administration and Senate liberals have gone onto a defensive [LINE ILLEGIBLE] challenging Helms in a direct vote. They will try to sidetrack the Helms amendment by asking the Senate to give Carter until June 30, at the latest to make his determination on the elections and the lifting of sanctions.

Under compromise legislation enacted last year, the president has to lift sanctions if he determines that a government has been installed through free and fair elections and has made a genuine effort to start negotiations with black nationalist forces that are waging an escolating guerrilla war against the Salisbury authorities.

The move to give Carter more time may also pick up support from Senate Republicans who think the Rhodesia question may emerge as a 1980 election issue. Prospective GOP challengers reportedly would like to see Carter go on the record against the Muzorewa government.

Reflecting their own concerns on that score, some of Carter's advisers have been urging him not put his prestige on the line in the battle over his innovative Rhodesia policy, which has been stalemated by the refusal of the Salisbury authorities and the Patriotic Front forces of Joshua Nkomo and Robert Mugabe to negotiate an end to the war.

Conservatives are expecting the report by the nine-member Freedom House observer team that included Lowenstein and Rustin to have particular impact in the Senate. The organization's 49-member board of trustees, which is chaired by former senator Clifford P. Case and which includes Sen. Jacob Javits (R-N.Y.), is due to decide Monday if it will attach a recommendation on sanctions to the report.

Case, a New Jersey Republican, and Javits coauthored last year's compromise legislation that set the "free and fair elections standard that has now become the key to the sanctions battle. Both are reported to be leaning toward some form of support for Muzorewa and Smith now.

Freedom House is a New York based private organization described by executive director Leonard Sussman as "a broad centrist group" interested in supporting "free institutions around the world." Among the board's members are Sen. Daniel Patrick Moynihan (D-N.Y.), a critic of the administration's approach to Rhodesia and Zbigniew Brzezinski, who is on leave from the board while serving as President Carter's national security affairs adviser.

Lowenstein, who went on two previous trips to Southern Africa in the last year sponsored by the State Department, has met with Brzezinski, his deputy David A. Aaron, Secretary of State Cyrus R. Vance and others to urge that the administration voice [WORD ILLEGIBLE] for Muzorewa if the [WORD ILLEGIBLE] leader moves to bring genuine majority rule to Rhodesia.

The active involvement of a former New York congressman who led the early stages of the campaign to deny the 1968 Democratic nomination to President Johnson has left a swath of conflicting impressions.

Black South Africans he saw in an earlier trip came away with the impression that Lowenstein was floating a new softer line on Southern Africa that Brzezinski Aaron and others in the administration privately support Lowenstein and spokesmen for the administration emphatically deny this.

Midlevel State Department officials, who report an unease within the department over Lowenstein's private diplomatic initiative, suggest that the former antiwar activist may be trying to carve out a role for himself in the administration by pushing "The Lowenstein Plan."

Adding both irony and credibility to Lowenstein's newly controversial position on Rhodesia is his long record as a vocal critic of South Africa's apartheid system. He was long banned from that country because of his contacts with black political leaders there and because of a book he wrote savagely attacking the government. On his most recent trip, however, he met with the nation's prime minister.

Senate liberals sought yesterday to counter the observer reports from Freedom House and more conservative groups by releasing separate analyses from the National Bar Association, hich represents black attorneys, the United Nations Association, and the Lawyers' Committee for Civil Rights Under Law. These reports conclude that the [WORD ILLEGIBLE] and conditions under which the Rhodesian elections were held made it impossible for them to be free and fair.

The reports were released by Sens. George McGovern (D-S.D.), and Edward M. Kennedy (D.MASS). They and Sen. Paul Tsongas (D.MASS), are expected to lead the Senate fight to defend the administration's policy and keep sanctions in place.

The Congressional Black Caucus and black leadership groups headed by Transafrica, a lobbying organization, are also increasing their efforts. Prosanctions activists argue that a unilateral end to the U.N. imposed boycott will shatter the administration's hard-won diplomatic gains in the Third World and open the way for greater participation by the Soviet Union and Cuba in Southern Africa