Because the states were complicit and Federal action was required. The Federal government lacks jurisdiction without specific laws. In one case, the Federal government was able to prosecute a Florida policeman. He was fined $1000.

From President Truman's Commission on Civil Rights, about two of the "less brutal" lynchings in 1946:

"On July 20, 1946, a white farmer, Loy Harrison, posted bond for the release of Roger Malcolm from the jail at Monroe, Georgia. Malcolm, a young Negro, had been involved in a fight with his white employer during the course of which the latter had been stabbed. It is reported that there was talk of lynching Malcolm at the time of the incident and while he was in jail. Upon Malcolm's release, Harrison started to drive Malcolm, Malcolm's wife, and a Negro overseas veteran, George Dorsey, and his wife, out of Monroe. At a bridge along the way a large group of unmasked white men, armed with. pistols and shotguns, was waiting. They stopped Harrison's car and removed Malcolm and Dorsey. As they were leading the two men away, Harrison later stated, one of the women called out the name of a member of the mob. Thereupon the lynchers returned and removed the two women from the car. Three volleys of shots were fired as if by a squad of professional executioners. The coroner's report said that at least 66 bullets were found in the scarcely recognizable bodies. Harrison consistently denied that he could identify any of the unmasked murderers. State and federal grand juries reviewed the evidence in the case, but no person has yet been indicted for the crime.

Later that summer, in Minden, Louisiana, a young Negro named John Jones was arrested on suspicion of housebreaking. Another Negro youth, Albert Harris, was arrested at about the same time, and beaten in an effort to implicate Jones. He was then released, only to be rearrested after a few days. On August 6th, early in the evening, and before there had been any trial of the charges against them, Jones and Harris were released by a deputy sheriff. Waiting in the jail yard was a group of white men. There was evidence that, with the aid of the deputy sheriff, the young men were put into a car. They were then driven into the country. Jones was beaten to death. Harris, left for dead, revived and escaped. Five persons, including two deputy sheriffs, were indicted and brought to trial in a federal court for this crime. All were acquitted.

These are two of the less brutal lynchings of the past years. The victims in these cases were not mutilated or burned."

Link to reference: https://www.trumanlibrary.org/civilrights/srights2.htm#20

One suspects the point was that a federal crime would be prosecuted by federal prosecutors, who would be less likely than the local county guy to be drinking buddies with local Klansmen.

Murder is targeted at one person and committed by one or a few people. Lynching is used to terrorize groups of people by other groups of people.