People were lynched in the American South because minorities were used as scapegoats for crimes that happened inside of communities. For example, in New Orleans, Italians and Irish were hanged when murders happened (famously after the death of Police Cheif Hennesy ( http://www.knowla.org/entry/1064/), and in Mississippi black people were lynched as scapegoats for rapes, with numerous documented examples, exemplified in the fiction book To Kill a Mockingbird.

Because vulnerable populations like Italians, Irish, Chinese immigrants, and black people were distrusted by the white community, they often bore the blame for unsolved crimes, no matter the legal outcome of the case. In the case of, Jesse Washington, ( https://en.wikipedia.org/wiki/Lynching_of_Jesse_Washington#CITEREFSoRelle2007 ) this meant actively attacking the courtroom as a mob. This was not so much as a derivation of pleasure, as you state, but a "fair" delivery of justice which the courts had failed to render in their view.

TL;DR the vulnerable populations were going to be blamed from the beginning, it didn't matter what the local court said.

There are a number of different historical arguments to be made regarding this tragic phenomenon. Personally, I think Amy Louise Wood comes closest to a well-rounded explanation of spectacle lynchings in Lynching and Spectacle. It's not that long and well worth the read if you're interested in this subject. Key to Wood's argument is the spectacle aspect of lynchings. Look through the contemporary photographs of lynch mobs in Wood's book and take careful note of who is in the crowd. The composition of the crowds are key to her argument that who's watching is what really matters in these events.

It's also important to remember that it wasn't just blacks who were lynched, and lynchings didn't just occur in the South (although they were the most numerous per-capita there.) I grew up in ND and MN and there are dozens of lynchings that occurred in those two states, which aren't where we would normally place lynchings. Minorities or outsiders of any kind were more vulnerable to be lynched since they could were easy scapegoats for crimes they may or may not have committed. In the South black men were particularly vulnerable to accusations of rape from white women. Some feminist historians have argued that lynchings of black men for the alleged rapes of white women was in fact meant as a means through which to exert social control over white females. (I'm not sure if I agree with that entirely, but it's an interesting argument.) I would definitely recommend Wood's book if you have time to read it.