The owner of Braniff Inc.'s 30 airplanes has sued the carrier in an attempt to prevent it from renting 20 of the planes to other airlines. Braniff announced plans to loan the airplanes out last week as part of a belt-tightening program in an attempt to save the troubled company.

Separately, Braniff slashed fares by as much as 75 percent, another part of its survival package, and named a new president to replace William D. Slattery, who resigned last week.

A Braniff spokeswoman declined to comment directly on the suit, filed against the airline in federal district court in Fort Worth by trustees for the BRNF Liquidating Trust, which owns the airline's planes on behalf of a number of the airline's creditors. Braniff leases the planes for $90,000 each per month from BRNF, which was set up last December under the auspices of the bankruptcy court in which Braniff filed for bankruptcy protection in May 1982. The airline was revived earlier this year under new ownership, but has continued to lose millions of dollars a month.

BRNF said in its suit that some Braniff creditors "object to Braniff's redeployment and consolidation plan" and want an injunction against subletting the aircraft until Nov. 19, when creditors are to meet to decide what to do.

The suit contends Braniff's agreement with BRNF prevents the airline from transferring or assigning the leases on its planes "without the express written consent" of the planes' owners. The Braniff spokeswoman, however, said the airline's lawyers believe the company's plans do not violate that agreement. Braniff has announced plans to rent 10 planes, with Braniff crews, to Northeastern International Airways of Fort Lauderdale, Fla., for about six months, and is negotiating with other airlines to rent the other 10 planes.

Braniff's remaining 10 Boeing 727s are flying a limited schedule between 10 cities. In an effort to drum up business on those routes, the company announced new low fares to the cities from its Dallas-Fort Worth base, effective for two weeks beginning Nov. 5. Braniff's chief competitors, American and Delta airlines, immediately announced that they would match the new fares on a limited basis.

Braniff's new president is Ronald Ridgeway, 38, a former Braniff executive who most recently has been chief operating officer of SMB Stage Line Inc., a Dallas-based cargo airline. Ridgeway was with Braniff from 1979 to 1983, and also worked for Trans World Airlines. His last position at Braniff was senior vice president of customer service.