The victim was found when the emergency services were called to reports of a man injured at a property on Beech Court in Workington at about 07:30 GMT.
A 22-year-old man was later arrested in the Northside area of the town.
A Cumbria Police spokesman said: "Detectives are currently carrying out inquiries in the area. We would like to reassure people that there is no perceived threat to the public."
A man has been arrested on suspicion of murdering a man in Cumbria.