The plane crashed on a field in Kägiswil after being swept off course while landing by storm winds, local daily Neue Luzerner Zeitung reported online on Wednesday citing witnesses.
Two occupants of the plane died at the crash site while a third man succumbed to his injuries overnight after being taken by helicopter to the Lucerne cantonal hospital for treatment, cantonal police said.
The crash occurred at 5.25pm, said police.
According to the Swiss news agency SDA on Thursday, the victims were a 67-year-old flight instructor, his 21-year-old pupil and a passenger. They are believed to have been on a training flight.
The three men all came from the canton of Obwalden. The victims all died of internal injuries.
A federal investigator is looking into the cause of the crash, along with federal aircraft accident commission authorities.
The accident occurred close to the Sarnen industrial area, which was hit by a fierce thunderstorm at the time, Blick reported online.
The newspaper said the plane was a single-engine Piper Cadet, owned by a flight school in Kägiswil.
Jost Vogler, manager of the Kägiswil airfield, told Blick that it was the first serious accident there in 20 years that he was aware of.