I favour judicial process, but not predefined sentences or formal collective enactment of them.
I believe it should be up to the person found guilty as to whether they agree to make restitution or not. If they do, then the slate should be wiped clean.
A person could still maintain their innocence, and contest the conviction, whilst complying with the verdict and making restitution, then later fighting to clear their name in the hope of being recompensed if they succeed in having the verdict overturned.
In the unlikely event that someone who has made restitution is lynched, there will be serious consequences, with the perpetrators being tried for murder.
In the event that someone had been found guilty, but has refused to make restitution is lynched, and the verdict is later found to be unsound, then those who performed the lynching would be tired for manslaughter.
Any would be lynchers would therefore have to be absolutely convinced of the persons guilt. Even then the lynching would have to be comparable to the offence.
The likelihood of lynchings is therefore low, and any that did occur would likely involve convicted murderers, who had refused to make restitution, and whose guilt was not disputed.
What’s wrong with that?