Thanks for acknowledging the injustice of police killing black folks. If there is any hope to all this, it will require that the majority come to this realization, especially people in power. Wouldn't it be great if the president would take a delegation and go talk to the people at the protest sites, ask them what are their grievances and how can we do better? After all, they're American citizens using their first amendment rights. The violence is a result of frustration over not being heard. (Also there's been some instigation from the counter-protesters; in fact, some people at the scene are saying that most of the violence is coming from the opposition, especially harming other people rather than harming inanimate objects.) I"m planning a series of tweets to get 45 thinking along these lines. Get out there, listen to the protesters, and make a deal!
Re lynching: it's true that the early 20th century version of lynching has fallen out of fashion. However, the key element of lynching as opposed to other types of murder is, as you say, the motivation by the perp(s), who are convinced that they are carrying out justice, even if it's the DIY sort.
This is the same motivation of cops who, trained to see themselves as warriors and civilians as enemy combatants, may forget their training in de-escalation and conflict mediation, and jump straight to the use of deadly force.
This is the same motivation of people who bring firearms to protests, and use them with deadly effect. ( It is noteworthy that those who do this are mostly right-wing, although recently a few lefties have gotten in on the act.)
This was the motivation of George Zimmerman, who armed himself and stalked Travon Martin against the advice of the 911 operator. Martin, spooked at being followed, turned around to face his harasser and defend himself. Things got ugly, the men came to blows as men often do, and Zimmerman killed Martin, claiming self defense. He got cleared, too -- even though, in most cases, you don't get to claim self defense if you started the trouble. This was what started the Black Lives Matter movement.
I, too, fear that the violence associated with some BLM protests may be counterproductive. This is especially so in view of the massive propaganda being pushed that those who oppose the current administration are traitors, thugs, anarchists, etc rather than fellow-Americans who don't like the way things are going at this time. But I'm not a tactician with BLM; in fact, I'm not even a voting member, so that's not for me to say. All I can do is raise my voice in support of those calling attention to injustice. I hope that we can start listening to the voices of oppressed people and develop real solutions to the problems that lay at the foundation of this country. When that happens, the violence will end, because people will no longer feel a need to get disorderly in order to be heard.