Final answer:
In the investigation into the murder of Lucy Welch, the local law enforcement agency, with detectives, a sheriff, or a county attorney, would be in charge, as inferred from the provided excerpts.
Step-by-step explanation:
The responsibility for the investigation into the murder of Lucy Welch would depend on the context provided by the references, which seem to be snippets from various literary sources and case studies. If we refer to a traditional legal process, the investigation usually falls under the jurisdiction of the local law enforcement agency and is overseen by a detective or a team of detectives.
The mention of a sheriff and county attorney in one of the excerpts suggests that local law enforcement and legal authorities are in charge. As for the 'how we know' part, we can infer that the investigation is typically a procedural standard in legal systems after a crime has been reported, as depicted in the provided extracts.