The 18-year-old was only able to complete 28 minutes of the Reds' 2-1 win over Chelsea in the Premier League 2 on Sunday, being replaced by 35-year-old Jay Spearing.
Doak has earned 10 senior appearances for Liverpool since joining from Celtic last year and would have been expected to make the squad for Wednesday's EFL Cup tie with West Ham United in the quarter-finals, having started the Reds' third-round win over Leicester City.
However, giving an injury update to liverpoolfc.com ahead of the visit of the Hammers, Lijnders confirmed that Doak had suffered a serious meniscus tear and will require an operation.
"That's not a good one. He tore his lateral meniscus, which needs surgery. That one will take [a] longer time. He is young, he is a fit guy, he is a positive guy so for sure he will come back stronger, and we need him to come back with the same fire he has with the ball, how he was. He can take time and we will wait for him," Lijnders said.
Doak has become the second Liverpool man to suffer a severe knee injury this month, as defender Joel Matip tore his ACL against Fulham on December 3 and has been ruled out for the remainder of the season.
Andrew Robertson (shoulder), Thiago Alcantara (hip) and Stefan Bajcetic (calf) are not expected to return from their afflictions until the New Year either, but Lijnders had a positive update to share on Ryan Gravenberch.
The Dutchman came off with a suspected hamstring issue during the weekend's 0-0 draw with Manchester United in the Premier League, but it has since been ascertained that he was merely suffering from fatigue and could be available for the quarter-final.
"We thought there was really something, he came off during the game and you saw immediately when he came off what that did to the team as well, he was playing really well. Especially against these man-marking sides he plays unbelievable," Lijnders added.
"But he had a scan and it's only DOMS, which is fatigue, so that's a really good thing. He will train hopefully today, let's see where he is. We have to be careful of course because that's a sign. So that's a good one."
Additionally, Lijnders is hopeful that Alexis Mac Allister will be able to return from his knee problem imminently, but he did not directly confirm whether the Argentine would be able to face the Irons.
"Alexis is progressing well, he doesn't have pain anymore, which is a good thing. It was worse than we first thought, but he is progressing well, no pain. Let's see if we can progress him," the Liverpool assistant explained.
Finally, Diogo Jota is slowly stepping up his recovery from the hamstring issue he picked up against Manchester City in November, but Lijnders has hinted that the Portuguese attacker will not be rushed back into action this week.
"Diogo is doing ball work on the pitch so that is getting closer and closer. But always with hamstring injuries you have to be careful, we always say when they come back give them another two or three days for sure," the 40-year-old said.
Should Liverpool get the better of West Ham on Wednesday, they will face one of Chelsea, Newcastle United, Everton, Fulham, Middlesbrough or Port Vale in the EFL Cup semi-finals.