The Biancocelesti last lifted the cup in 2019, and they now kick off their campaign in the competition's last 16, which Genoa reached with two narrow wins earlier this season.
After a run of one point from three league matches had seen Lazio slip down the Serie A standings, last week's Champions League victory over Celtic signalled a change in fortunes for the capital-city club.
Taking them into the competition's knockout phase, captain Ciro Immobile's late brace from off the bench guided his team past the Scottish champions, and just a few days later, the Biancocelesti returned to winning ways domestically.
Despite later wasting several chances, Lazio held preserved a lead gained after eight minutes at home to Cagliari, as Pedro latched on to a pass from Manuel Lazzari - when the visitors went down to 10 men just before the half-hour mark, victory was all but assured.
Maurizio Sarri's men still sit adrift of Italy's top four, but having got their league campaign back on track, they now turn their attention to the Coppa Italia.
Eliminated by Juventus in the quarter-finals last season, Lazio are aiming to reach the last eight again by beating Genoa on Tuesday, just three months on from when the clubs last met in Rome for their second Serie A game of the season.
On their most recent trip to Stadio Olimpico, Genoa upset the odds and left with all three points, as they held Lazio at arm's length after Mateo Retegui struck in the 16th minute.
Since then, the promoted side have gone on to establish themselves in mid-table upon their Serie A comeback, and Saturday's 1-1 draw at home to Empoli left them only five points behind their Coppa Italia opponents in the table.
Although 20 other attempts failed to find the goal-frame, Ruslan Malinovskyi scored from Genoa's sole shot on target, but Matteo Cancellieri's second-half equaliser then denied Alberto Gilardino's side a fourth league win at Marassi this season.
Before continuing their quest to stay afloat amid Calcio's elite, with Sunday's game in Monza their next top-flight engagement, the Grifone return to the cup, which they have won just once before, way back in 1937.
Following a season-opening 4-3 defeat of Modena at Stadio Luigi Ferraris, they then beat Reggiana in the second round at the start of November, as Albert Gudmundsson scored a 99th-minute extra-time winner to book a place in this week's last 16
Amid a packed schedule at home and in Europe, Lazio boss Maurizio Sarri is set to make several changes to his starting lineup in midweek, with some fringe players handed a chance to impress.
Though Nicolo Casale is close to returning from an adductor injury that has seen him miss seven matches so far, Tuesday's game comes too soon; centre-back partner Alessio Romagnoli remains sidelined by a calf problem. Therefore, Patric and Mario Gila could continue at the heart of the hosts' back four.
Genoa, meanwhile, welcomed Mateo Retegui and Junior Messias back to action against Empoli, but Albert Gudmundsson, Mattia Bani and Kevin Strootman - the latter of whom is ruled out until 2024 by a hamstring injury - are all unavailable to coach Alberto Gilardino.
Following his trademark strike on Saturday, Ruslan Malinovskyi will miss the Grifone's upcoming trip to Monza due to a Serie A suspension but is expected to start at the Olimpico.
Lazio possible starting lineup:
Sepe; Hysaj, Patric, Gila, Pellegrini; Kamada, Cataldi, Vecino; Isaksen, Castellanos, Anderson
Genoa possible starting lineup:
Martinez; De Winter, Dragusin, Vogliacco; Hefti, Thorsby, Kutlu, Malinovskyi, Martin; Puscas, Retegui
We say: Lazio 2-1 Genoa
Setting up a potential Derby della Capitale clash in the quarter-finals - where arch-rivals Roma will await if they can overcome second-tier Cremonese - Lazio should make the most of home advantage to knock out Genoa, whose main goal is Serie A survival.
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