Lulic - a second-half substitute for Stefano Pioli's side - turned in Felipe Anderson's cross with just 11 minutes to play at Stadio San Paolo to book the six-time winners a spot in the June 7 showpiece against Juventus.
The final will be staged at Lazio's Stadio Olimpico home, as they go in search of a third Coppa Italia success in seven years.
Coppa holders Napoli will feel hard done by after dominating much of the second leg, with Manolo Gabbiadini - who scored their goal in the 1-1 first-leg draw - coming closest when his excellent free-kick struck the post.
Lazio defended well but star Napoli forward Gonzalo Higuain had an off night in front of goal and it proved costly as Lulic had the last laugh before making sure of their progression with a heroic goalline clearance to deny Jose Callejon a tap-in.
A delighted Pioli led the visitors' celebrations at the final whistle as the Lazio coach goes in search of silverware to add to a campaign that looks set to end in UEFA Champions League qualification for the first time in eight seasons.
Napoli boss Rafael Benitez insisted his side would not sit back despite their away goal in the first leg and they made all the early running.
A heavy touch robbed captain Marek Hamsik - back in the starting XI after being left out against Roma on Saturday - of space to get a meaningful shot off following Dries Mertens' clever pass.
Napoli fans then thought they had scored when Gabbiadini's superb 25-yard free-kick bent over the wall and dipped, with goalkeeper Etrit Berisha beaten, but his effort cannoned off the post as Napoli failed to make their dominance pay.
Only superb last-ditch defending in the 51st minute from Dusan Basta denied Higuain - who was set to tap in Christian Maggio's cross unmarked at the far post.
Much of Lazio's attacking threat came from either Miroslav Klose or Antonio Candreva, and the latter registered their first shot on target in the 54th minute before the German veteran saw penalty appeals fall on deaf ears after bustling into the area.
Having committed numbers forward, Lazio were caught out by a breathtaking Napoli counter-attack, but Higuain's poor first touch allowed the onrushing Berisha to claim the ball.
It served as a warning, and in the 79th minute, Anderson's deflected cross from the right beat goalkeeper Mariano Andujar but not Lulic, who simply side-footed in from four yards.
Higuain volleyed way wide as Napoli desperately sought an equaliser, and it nearly came after substitute Lorenzo Insigne charged forward down the left, but Lulic was on hand to deny Callejon with a crucial intervention that capped his superb cameo.
