While Sergei Semak's side have lost both of their first two games in the section - at home to Club Brugge and away to Borussia Dortmund - their Roman visitors are joint-top on four points, thanks to a 3-1 home win against Dortmund and last week's draw in Bruges.
Defeat in Dortmund was followed for Zenit by a 2-0 win away to Khimki in the Russian Premier League on Sunday - a result which leaves them just above several Moscow clubs at the top of the table.
Zenit claimed their seventh league title in 2019-20 - their second in a row and their previous six triumphs have all come since 2007. They also added the Russian Cup to complete the club's second ever domestic double. However, continental success has proved harder to come by.
The St Petersburg side have, in fact, won only three of their last 13 European matches, losing nine, and only recorded two victories in their last 11 Champions League games.
Last season Zenit finished fourth in their section, behind RB Leipzig, Lyon and Benfica, despite picking up seven points from their six matches.
They are now in significant danger of missing out on the last-16 again, being sorely in need of points from their back-to-back fixtures with Lazio.
Lazio's record is not greatly superior though - the opening day win against Dortmund was only their second in 13 games at this level. Remarkably, last week's game against Brugge - against the unsettling backdrop of a major pre-match COVID-19 breakout in the squad - brought Lazio's first draw in 19 European fixtures.
Though Lazio were missing a number of their leading players, such as prolific striker Ciro Immobile and midfielders Luis Alberto, Manuel Lazzari and Lucas Leiva, they were the sharper side in the early stages and were rewarded after 14 minutes when Joaquin Correa curled a well-taken opening goal into the corner of the net. However, Brugge grew into the game and were deserving of their point at the end of 90 minutes.
On domestic duty at the weekend, the Biancocelesti tackled struggling Torino. Simone Inzaghi's side salvaged a thrilling 4-3 win - coming from behind twice and scoring two injury time goals - to snatch the points against all odds.
Lazio, then, are on a four-game unbeaten streak - winning three - despite dealing with widespread illness and injury. Now, with several of their tests proving 'false positives', a number of their missing men have returned in time for the long journey east.
These two sides have never met before and Lazio - despite featuring regularly in Europe - have not faced a Russian club since the turn of the century.
For rarity value alone, then, it is set to be an intriguing tussle, with the Russian champions also in dire need of maximum points to save their Champions League campaign.
Zenit St Petersburg Champions League form: LL
Zenit St Petersburg form (all competitions): DWLLLW
Lazio Champions League form: WD
Lazio form (all competitions): DLWWDW
On Saturday, Lazio announced that their entire squad would be placed into quarantine, due to multiple cases of COVID-19.
It was unclear exactly who had tested positive - as the club claimed to be following protocols - but the majority of those missing in Bruges, last week, returned on Sunday. Luis Alberto and Manuel Lazzari were both absent and are not expected to travel for Simone Inzaghi's side.
The hosts, who can welcome up to 16,000 fans into the stands - in accordance with Russian government and UEFA guidance - are without ex-Barcelona winger Malcom with a knee injury and are facing the potential absence of star striker Sardar Azmoun through illness.
Zenit St Petersburg possible starting lineup:
Kerzhakov; Karavaev, Lovren, Rakitskiy, Santos; Barrios; Erokhin, Kuzyaev, Wendel, Driussi; Dzyuba
Lazio possible starting lineup:
Strakosha; Patric, Felipe, Acerbi; Marusic, Milinkovic-Savic, Leiva, Akpa-Akpro, Fares; Correa, Immobile
We say: Zenit St Petersburg 1-2 Lazio
Champions of Russia, Zenit must capitalise on home advantage to take their first points of the group stage - or effectively face an early exit.
Despite a wildly fluctuating start to the season, Lazio have proven they are made of sterner stuff, though. This battle of the sky-blues is set to go the way of the Biancocelesti, with Ciro Immobile back in time to lead the line.