If you are using the word "lynch mob" in a rhetorical way to refer to people who are not depriving you of life, liberty, or property, arguments about actual lynch mobs do not apply. A so-called "lynch mob" that merely has opinions about you and does not do anything to you is not unjust any more than a high school mock trial club is unjust. A so-called "lynch mob" that has opinions about you and goes on to do entirely legal things, like exert their free speech rights to publish their opinions about you, is not unjust, either.
historical data support my claim as wikipedia points: "Public humiliation is the dishonoring showcase of a person, usually an offender or a prisoner, especially in a public place. It was regularly used as a form of punishment in former times, and is still practiced by different means in the modern era."
The right about trials is about a fair trial by the government, and is a check on the government's power to punish.