While the hosts are back among Europe's elite for the first time since 2021, Atleti are mainstays in the continent's top club competition - but they were eliminated in the group stage last season.
Rewarded for their consistency at the end of last term, Lazio slipped past several other contenders to finish distant runners-up to Italian champions Napoli, securing a return to Champions League football after dipping their toes in both the Europa League and third-tier Conference League.
Maurizio Sarri's side built their success on numerous clean sheets and the coach's familiar possession-based principles, but they have started the 2023-24 campaign in less impressive fashion.
Heading into a much-anticipated Group E campaign, in which Celtic, Feyenoord and this week's visitors Atletico Madrid will be their rivals for a top-two finish, Lazio sit on just three points from four Serie A matches and have conceded at a rate approaching two goals per game.
Curiously, the Biancocelesti began with back-to-back defeats - losing to Lecce and Genoa - before beating the Scudetto holders in Naples just before the international break; their return to action at the weekend saw them suffer another chastening defeat.
Two weeks after summer signing Daichi Kamada scored a deserved winner against Sarri's old club Napoli, a trip to Turin ended in a 3-1 Lazio loss, as Juventus stormed into a two-goal lead before the half-hour mark and Luis Alberto's clinical second-half strike proved only a minor consolation.
They must swiftly turn their attention to Champions League matters now, and will aim to at least replicate their most recent adventure in Europe's top club tournament, back in the 2020-21 season: that year, Lazio made it through their group before falling to Bayern Munich in the last 16.
The home side's notorious fans will welcome a familiar figure back to Stadio Olimpico on Tuesday night, as former Scudetto-winning midfielder Diego Simeone will lead out Atletico Madrid - the club he has since become synonymous with.
While these teams have not met for 11 years, Simeone will still remember those encounters well, as in his first European tie the Argentinian guided Atleti to victory over the club he once won the Serie A-Coppa Italia double with as a player.
At the end of that season, Atletico held the Europa League trophy aloft, but they have yet to lift the big one despite several bold attempts - most notably, final losses to city rivals Real Madrid in both 2014 and 2016.
Los Colchoneros now aim for a fourth final appearance overall; however, they do so on the back of a result that came as an unwelcome bolt from the blue.
Just before international football intervened, Simeone's side had hammered Rayo Vallecano 7-0 - Atletico's biggest ever away win in La Liga - and then seen their subsequent fixture against Sevilla postponed. Resuming with a shock 3-0 loss to Valencia on Saturday, though, may cause doubts ahead of their Champions League return.
Casting a shadow over Simeone's long-term future, Atleti finished bottom of their group last term, so with the Madrid derby to come next weekend, the coming days could prove crucial in setting the tone for the months ahead.
As Lazio should have a full complement of players available on Tuesday, coach Maurizio Sarri may make some changes to his starting XI, after retaining the same team for games against Napoli and Juventus.
Sarri could therefore introduce summer signing Matteo Guendouzi in central midfield, with the former Marseille man pushing for his first start since joining on a season-long loan.
By contrast with their hosts, Atletico are enduring plenty of injury problems early in the season, and after their La Liga loss to Valencia at the weekend it emerged that Thomas Lemar could be ruled out for several months after suffering a serious Achilles tendon injury.
After Yannick Carrasco left for Al-Shabab, Rodrigo Riquelme filled in on the left flank on Saturday, but either Javi Galan or Samuel Lino may be brought in at Stadio Olimpico. Meanwhile, Alvaro Morata and Antoine Griezmann should be paired in attack.
Lazio possible starting lineup:
Provedel; Marusic, Casale, Romagnoli, Hysaj; Guendouzi, Cataldi, Alberto; Anderson, Immobile, Zaccagni
Atletico Madrid possible starting lineup:
Oblak; Molina, Azpilicueta, Witsel, Savic, Galan; Saul, Barrios, Llorente; Griezmann, Morata
We say: Lazio 1-2 Atletico Madrid
Both teams have suffered tough defeats following the international period, so confidence will not be sky-high in either camp. Lazio's sluggish start to the new season has come as something of a surprise, but their defensive instability could see Atletico sneak a valuable first-day away win.
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