Mr Lee, his pregnant wife and Sudanese driver were set on by around 20 gunmen. Mr Lee was hit in the chest and throat and died six hours later in hospital.
Captain Paddy Ankunda, a spokesman for the Ugandan army, blamed the attack on rebels of the Lord's Resistance Army.
The LRA comprises the remnants of a northern Ugandan rebellion that began in 1986.
In the past the rebels have operated from bases in the south of Sudan.
Last month, the rebels were also blamed for killing two aid workers and wounding four others in separate ambushes in northern Uganda.
The driver, Karaba Juma, was also hit and injured during the latest attack and the car came to a stop.
It is unconscionable that the LRA is carrying out these vicious attacks on unarmed humanitarian workers
The gunmen threatened to set the vehicle on fire with Mr and Mrs Lee and their driver still inside, but Mrs Lee stayed with her husband - who was not killed immediately - and persuaded the rebels not to burn them alive.
They were allowed out and their Land Cruiser was burned.
Mr Lee, who was still alive, was taken to hospital in Yie where he died at 2220 local time on Saturday, six hours after the attack.
Mrs Lee, 35, who is from Paraguay, was unharmed in the attack and is now recovering in hospital in Uganda.
Mr Lee, who was trained in trauma counselling, was born in Bermuda, an overseas British territory, and lived there.
As a result, he was a British national but is not thought to have had any close relatives in Britain.
Andreas Zetterlund, a spokesman for IAS, said: "We are not sure what kind of group the gunmen were from but we suspect it could be the Lord's Resistance Army but we don't have any confirmation."
Last month two aid agencies suspended their work in Uganda's north after the LRA killed two aid workers in attacks.
In the aftermath of these attacks, Jan Egeland, United Nations Under-Secretary-General for Humanitarian Affairs and Emergency Relief Co-ordinator, said: "It is unconscionable that the LRA is carrying out these vicious attacks on unarmed humanitarian workers.
"The people of northern Uganda are heavily dependent on humanitarian aid, and access to them is already precarious.
"These attacks threaten the provision of life-saving assistance to nearly 1.7m people."
The LRA has terrorised civilians in the region through a campaign of murder, mutilation and child abduction.
Joseph Kony, the LRA's leader, faces 12 charges of crimes against humanity, including sexual enslavement and war crimes charges, under indictments brought by the International Criminal Court.
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