What is the etymology of the word lynch?

This is an eponymous word; that is, it comes from the name of a person. That person was William Lynch, who lived in Virginia in the late 18th century, and who, in 1780, got together with his neighbors to form a vigilante committee to uphold order in their town. They were apparently not known for providing fair trials to those they deemed transgressors, but their victims were not necessarily put to death. By 1811, the term Lynch law was used to describe such unfair tactics, and around 1835 the term was Lynch. By 1839 the upper case L was changed to a lower case one. In the late 19th century the verb form had come to mean “inflict a sentence of death without a lawful trial”. Today we more often hear the back formation lynching as the noun.

The word ‘lynch’ always makes me think of hanging, so I personally wouldn’t recommend using it in a case like this. But that may be an Americanism. You raise a good question, does the word carry unescapable connotations of hanging in UK English?