The fire in the Lahore Development Authority building on Egerton Road erupted at about 11.30 AM.
The blaze was reportedly caused by a short circuit on the seventh floor.
The building has offices of the department that manages the land records of Lahore city.
One man fell to his death while trying to climb to the roof to escape the flames within the building.
Two men succumbed to injuries they sustained when they jumped from the seventh floor, officials and witnesses said.
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Dozens of people were trapped within the building till the fire was extinguished in the evening.
Fire fighters took over five hours to control the blaze.
Footage on television showed people trapped on the upper floors standing at windows and waving at rescue teams as thick black smoke billowed out of the building.
The Pakistan People's Party alleged that those involved in land grabbing under the previous PML-N government led by Punjab Chief Minister Shahbaz Sharif were behind the fire.