Visiting Siena, who are currently bottom of the Serie A table, posed a greater attacking threat during the second half and with 56 minutes played they took the lead.
Lazio defender Michael Ciani attempted a clearance from close to his own goal following a parried save by Juan Pablo Carrizo. However, he only succeeded in striking his teammate Cana and the ball bounced back into the home team's net.
As the match drew to a close Lazio pushed forward in search of an equaliser, but it looked as though Seina would hold firm to book their place in the final eight of the competition.
Their resistance was broken in the fifth minute of stoppage time though as Ciani rose highest inside the area to head in for Lazio, thus forcing the match into an extra 30 minutes in the process.
Neither team was able to find the net during extra time and as a result penalties were required to determine who would reach the final eight of the competition.
Lazio converted all four of their kicks, while Larrondo missed a crucial shot for the away side, who were eventually defeated 4-1.