Clue by Clue: The Grave Robber Solution
The chauffeur stole the coin and put it in John Leigh’s clothing. He would have known about the coin and probably saw where Frank kept it. When he heard that Frank was dead, he took it. When he saw Lucy coming down the hall, he realized she would notice it missing and that he might be searched. So he hid it in the clothes of a patient who had already died—in this case, John Leigh. He then went and dug him up to steal the coin.