Sergei Milinkovic-Savic scored the first goal eight minutes from the end with a header after a corner before Joaquin Coria scored the second goal of an individual attempt at the break.
It is the seventh time that Lazio has won the Italian Cup and the first since 2013.
The Italian capital's victory ended four years of Juventus dominance over the local cup competition.
It also gave Lazio a place in the group stage next season.
Atletico defeated the Italian Cup for the first time since 1963, after their first season of the season.
Neurosurgeons have suffered from the start, but Atlante had the best chance in the first half when Martin de Rhone hit a player and turned to hit the post.
Lazio went on after Milinkovic-Savic took a corner in the net a few minutes after he was eliminated.
Korea then reached the score in the congestion time after going through the defender and dribbled over the goalkeeper and ended the ball in the net from close range.