Jason McCue, from East Kilbride, was found injured in John Hastie Park, Strathaven, on Tuesday afternoon. He died while being treated by paramedics.
On Thursday, a 50-year-old man appeared in court charged with murdering Mr McCue.
A 27-year-old man is currently in police custody and is expected to appear at Hamilton Sheriff Court later.
A second man has been arrested over the death of a 43-year-old man at a park in South Lanarkshire.