Three suspects were arrested this weekend in three southwestern cities in the shooting death of flamboyant El Paso lawyer Lee A. Chagra, whose murder touched off a federal investigation into drug and prostitution traffic along the U.S.-Mexican border.

Arrested by the FBI in Las Vegas on Saturday was Luis Fred Esper, 57, the uncle of an attorney who once was associated in legal cases with Chagra. A high-stakes gambler whom many considered the southwest's premier defense lawyer for accused narcotics violators, Chagra was slain last December.

Esper was taken into custody the day after El Paso detectives arrested Army Pfc Donald White, 21, a Californian stationed at Fort Bliss in El Paso, on the minor charge of driving with epired dealers' tags. The detectives reportedly found a tennis bag in White's car similar to a bag in which Chagra kept large amounts of money. Chagra's bag was missing after he was shot to death in his plush new office two days before Christmas.

Another arrest was made Saturday by the FBI in Los Angeles, also of a Fort Bliss soldier from California. He was identified as Spec. 4 David L. Wallace, 20.

Both Esper and Wallace were held on federal charges of interstate transportation of stolen money and unlawful flight to avoid prosecution for murder. White was booked on murder charges in El Paso and held on $200,000 bond.

After Chagras' murder his office was sealed and his files inspected by police, who acknowledged sharing some of their information with federal officials. Family members, including lawyer Joe Chagra, charged that authorities were rummaging through the files to get evidence on the salin man's clients and associates.

Whether or not this happened, the Chagra killing did touch off a U.S. grand jury investigation. Last week the FBI announced it planned a major sweep of El Paso businessmen involved in narcotics and prostitution traffic.

Special agent O. Leon Dobbs, saying the FBI is "going to make an example of a few investors," urged El Paso businessmen to come forward and tell what they knew of illegal activities in their city.

Lee Chagra, a popular lawyer with a sympathy for the underdog, was a frequent target of federal investigators who suspected that his role in narcotics traffic execeeded that of legal defender. He was indicted for drug smuggling in 1973; the indictment was dismissed.

Federal law enforcement officials also have been probing the affairs of Jimmy Chagra, a high-rolling Las Vegas gambler who, like his older brother Lee, has won or lost thousands of dollars on the turn of a card. Jimmy Chagra was indicted last week in Midland, Tex., on drug conspiracy charges involving cocaine and marijuana.