Last season's runners-up currently sit one point clear at the top of a fiercely-contested group and will know that dropped points could prove costly with Paris Saint-Germain and Napoli still to come.
Red Star's elation at reaching the group stages of the Champions League for the first time would have been tempered by the original draw, and the past two matches have accentuated the harsh reality of their standing in Group C.
The Belgrade outfit may be the most successful team in Serbia, but they never looked like standing a chance against the likes of Liverpool, PSG and Napoli.
So it has proved on matchdays two and three, with Red Star shipping 10 goals in those two games alone to find themselves with the worst defensive record - as well as the joint-worst attacking record - in the competition.
Tuesday night offers the chance to get a measure of revenge on Liverpool for the 4-0 drubbing they received at Anfield a fortnight before, and it is at home where they will expect to give their more illustrious opponents a bigger test.
It has certainly been that way so far, with Napoli - Liverpool's conquerors on matchday two - only managing a goalless draw on their visit to Belgrade as Red Star got their campaign off to a positive start.
Liverpool are the first team to visit in Europe since then, and Red Star have only lost one of their last 14 European matches in front of their own fans - although that did come at the hands of English opposition in the form of Arsenal last season.
Indeed, that Europa League defeat to Arsenal - which came more than a year ago in October 2017 - remains their most recent home defeat in any competition, winning 23 and drawing five of their 28 home outings since.
Despite their results in the Champions League so far, Red Star are also a team with a winning habit having taken 43 points from a possible 45 domestically this season to sit nine points clear at the top of the table after just 15 games.
European competition is a different matter entirely, though, and despite making it through qualifying for the first time, Red Star are actually winless inside 90 minutes in their last seven Champions League games this season - a run which stretches back to the beginning of August when they beat Lithuania's Suduva in the second qualifying round.
Home advantage looks to be their best bet in their attempts to end that run, but it would take a sizeable improvement from their Anfield display two weeks ago for them to get anything out of Tuesday's match.
Recent Champions League form: DLL
Recent form (all competitions): WWLWWW
Wherever Liverpool turn at the moment, they seemingly find themselves in a three-way tussle for top spot.
It is the case domestically, where Manchester City and Chelsea joined them in making it 11 games unbeaten at the start of the Premier League season, and also in their highly competitive Champions League group.
Things fell very kindly for the Reds on matchday two, with their convincing 4-0 win over Red Star being coupled with a late PSG equaliser against Napoli which saw Jurgen Klopp's side move top of the group.
Still, only two points separate the top three and Liverpool will know that maximum points from their matches against Red Star are imperative ahead of their upcoming games against PSG and Napoli.
Mohamed Salah shone as Liverpool completed the first leg of the attempted Red Star double, and since then Liverpool have also cruised past Cardiff City before being held to a 1-1 draw by Arsenal at the Emirates Stadium.
Saturday's result in North London saw Liverpool slip down to third in the Premier League table, but it was still a satisfactory point away to one of their big-six rivals as the Reds made it five games unbeaten since their late loss to Napoli on matchday two.
The defeat in Naples was Liverpool's second away European loss on the bounce, and they have now won just five of their last 20 such matches, with eight draws and seven defeats in that time too.
In all competitions it is only one win in their last four away games for Liverpool, although the loss to Napoli is their only defeat on the road so far this season.
With at least one of Napoli or PSG guaranteed to drop points on Tuesday, Liverpool will know that victory could put them as many as three points clear of their rivals going into that tricky closing double-header, leaving qualification for the last 16 firmly in their own hands.
Recent Champions League form: WLW
Recent form (all competitions): LDWWWD
Liverpool have confirmed that Xherdan Shaqiri will not travel to Serbia due to concerns over the reception he would receive due to his Albanian roots.
Klopp must also decide on whether or not to start Fabinho in midfield again after his performance against Arsenal was criticised in some quarters.
Red Star, meanwhile, are still expected to be without captain Vujadin Savic, who was an unused sub at Anfield but has not featured since being taken off at half time against PSG.
El Fardou Ben Nabouhane was the main reason Red Star made it through the qualifying stages, and his goal in a win over Proleter on Saturday was his first since September 2.
Richmond Boakye is another one to watch for Liverpool, having scored five goals in four league appearances this term.
Red Star possible starting lineup:
Borjan; Stojkovic, Degenek, Babic, Gobeljic; Krsticic, Jovicic; Ben Nabouhane, Ebecilio, Srnic; Boakye
Liverpool possible starting lineup:
Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Milner, Wijnaldum, Keita; Salah, Firmino, Mane
Head To Head
Tuesday's match will be the fourth time these two sides have met each other, with last month's match at Anfield the first Liverpool have won.
Prior to that, Red Star had won both matches 2-1 in the second round of the 1973-74 European Cup.
We say: Red Star 0-2 Liverpool
Liverpool are unlikely to find things as easy as they did at Anfield, but they should still have the quality to come away with a win from this game. Trips to Eastern Europe are not quite as gruelling as they once were in these competitions, and Klopp will also know just how important picking up all three points will be.