Well, part of this question is fact-based (is it true there was no federal prohibition against murder?), and part of it is speculative (why didn't this come up previously?). I'll do my best to answer each accordingly:

There was a federal statute against murder, prescribing the death penalty for it, in place prior to the shooting of Kennedy. It was used in the conviction and execution of Charles J. Guiteau for the murder of president Garfield. This statute however, section 5339 of the Revised Statutes of the United States, only could be applied for crimes committed on land under federal jurisdiction. Because Garfield was shot in Washington, DC, which was a federal district, the statute was applied. It does appear there was not a federal statute against murder in areas outside of federal jurisdiction, as that was up to the states to handle. As such, Oswald could not have been federally tried for murder, given the location of his crime. The federal statute covering assassination of a president is 18 USC 1751, which was published in August 1965, a bit under 2 years after Kennedy's death.

Moving to the second part, which is speculative, we have two more presidential assassinations we can compare to - Lincoln and McKinley. If we look at the Lincoln assassins, they weren't tried for murder either... they were tried for treason, and executed for same. While that treason was defined as the murder of the president in that particular case, murder wasn't legally the charge. The Lincoln assassination happened during wartime, which might have made it a bit more acceptable of a charge to use, but it is certainly conceivable that had no other route been available to get a death penalty, especially given the cold war situation, Oswald might have been tried for treason as well. There is no way to know for sure. 18 USC 2381 covers the modern version of treason.

As for McKinley's assassin, Leon Czolgosz, he committed his crime in New York and was taken down by a mob, and his victim, McKinley, called out to try and prevent a lynching info!. He was tried for murder under state law, and the state in question (NY) having the death penalty, was very rapidly executed.

At the time of McKinley's death, very few states did NOT have the death penalty, and even some those that had abolished it for most crimes kept it for treason, a charge which, as mentioned above, could be leveled if needed. I would imagine that it is highly likely it didn't come up, because few people conceived of a time when the death penalty wouldn't be readily available, and reading up on those sources, none of the assassins of presidents to date lived even a year after their crime.