The thing about lynching that makes it different from murder was that it was not necessarily about merely murdering someone. They were public spectacles that were attended by as many as 7000 people, and their purpose was to keep an entire class of people from getting uppitty, or exercising their constitutional rights: and sometimes it was for the grave offense of opening a store on mainstreet.
From 1880 - 1960 I believe it is estimated that upwards of 5000 people were lynched with the tacit approval of local and state governments that didn't believe that the 14th amendment applied to them. It was murder, yes, but the Congress gave no recourse to those deprived of "life, liberty, or property, without due process of law."
So to say it is merely like a "hate crime" law is to ignore the systemic problem that the south dealt with for a century. NOBODY was prosecuted, because it wasn't considered murder.