No peace for the wicked means that someone's heavy workload or lack of tranquillity is punishment for a sinful life, and this is what the person who was stared at with vengeance deserved.
Consider the statement "After the pleasantries were over, they started on me with a vengeance, which is what people who have done something bad deserve.". Is the statement "After the pleasantries were over, they started on me with a vengeance, no peace for the wicked." false? Yes/no/unknown