The visitors, meanwhile, are still aiming to reach the final of Germany's domestic cup for the first time in their history.
Match preview
Lubeck have actually gone as far as Mainz have in the DFB-Pokal, when they agonisingly lost to eventual champions Werder Bremen after extra-time in the semi-finals of the 2003-04 season.
Lukas Pfeiffer's side shocked second tier outfit Hansa Rostock to set up a second round tie with their forthcoming Bundesliga opponents this season, with Stadion an der Lohmühle set to be at full capacity when Mainz head into town on Tuesday.
Lubeck finished fifth in the fourth tier of German football last season, failing to gain an instant promotion back to 3. Liga following their relegation at the end of the 2020-21 campaign.
They have opened up a six-point lead at the top of the table this time around, though, having gained an impressive 30 points from 12 matches. As such, they will fully believe that they can cause another cup upset this week.
Mainz will be more confident themselves after ending a winless run of four matches by beating Werder Bremen 2-0 away from home on Saturday.
Only reigning champions Bayern Munich had scored more goals than Bremen heading into the weekend, but Bo Svensson's side became only the second team to shut them out this season in a textbook away performance.
Marcus Ingvartsen bagged for the second game running to provide his team with a narrow half-time lead, before Lee Jae-sung essentially settled the match six minutes after the hour mark.
Mainz comfortably dispatched Erzgebirge Aue 3-0 in the first round of the DFB-Pokal at the end of July, and Svensson will be hoping for a similarly professional performance against Lubeck - who are one division lower than Erzgebirge - on Tuesday as the 43-year-old looks to mastermind a serious cup run this season.
Lubeck DFB-Pokal form:
W
Mainz 05 DFB-Pokal form:
W
Mainz 05 form (all competitions):
W
L
D
L
D
W
Team News
Lubeck look set to be without Eric Grundemann, Jose Aguirre, Florian Egerer and Mats Facklan due to injury for the visit of Mainz on Tuesday.
Captain Tommy Grupe, who kept a clean sheet against his former side Hansa in the previous round, will lead the defence as they look to win against all the odds once again.
Mainz, meanwhile, may travel without Maxim Leitsch, Stefan Bell, Marlon Mustapha and club captain Silvan Widmer due to injury.
With his side facing FC Koln in the Bundesliga only three days later, Svensson could rotate accordingly, with the likes of Aymen Barkok, Angelo Fulgini and Anthony Caci all set for starts after appearing from the bench at the weekend.
Lubeck possible starting lineup:
Kirschke; Kolle, Grupe, Lohden, Rudiger; Boland, Plume, Gozusirin; Hauptmann, Drinkuth, Farrona-Pulido
Mainz 05 possible starting lineup:
Zentner; Schulz, Kohr, Hack; Da Costa, Barkok, Tauer, Caci; Fulgini, Burkardt; Onisiwo
We say: Lubeck 0-2 Mainz 05
We expect Mainz to build on a professional performance in Bremen at the weekend by securing another important victory away from home.
Lubeck are likely to make it difficult for Svensson's side, who should have too much quality and discipline to succumb to a shock defeat.