A win will wrap up a top-two spot for the Magyars, whereas Lithuania must win and hope that Serbia lose to Montenegro to stand any chance of qualifying for next summer's tournament.
Match preview
Lithuania go into this game with an impressive 2-0 away win in Bulgaria on Saturday evening, albeit the hosts made life easier for the away team as they had to play with 10 men for the entire second half.
Edgaras Jankauskas's men started slowly and looked rather cautious, but gradually got better as the game progressed and had a couple of good chances to take the lead before the sending-off.
First, Vykintas Slivka had an excellent chance through on goal after a delightful pass from Fedor Cernych, but his shot from close range was well saved by Ivan Dyulgerov.
Moments later, the Lithuanians had another chance when Torino midfielder Gvidas Gineitis entered the Bulgarian penalty area, but his powerful left-footed shot went just wide of the left post.
In the 42nd minute, Andrian Kraev was cautioned for the second time after a foul on Justas Lasickas, which subsequently saw him sent off, and Pijus Sirvys scored his first and second goals for the national team within 10 minutes.
It was Lithuania's first competitive win in over two years, having last beaten the same opponents Bulgaria in 2021 in FIFA World Cup qualifying.
However, the home record is a big problem for Jankauskas and his team, as the Lithuanians are currently winless at home for nine games, including international friendlies, and it is very unlikely that they will be able to end that streak on Tuesday night, as a win against the group leaders is too big a challenge.
Hungary, meanwhile, are now in pole position to finish first in Group G after a hard-earned 2-1 home win over Serbia on Saturday.
Two first-half goals from Barnabas Varga and Roland Sallai secured Marco Rossi's side their fourth win of Euro 2024 qualifying and they now have a three-point lead over second-placed Serbia with a game in hand.
Hungary are one of the few teams still unbeaten in qualifying and will be looking to extend that record with another positive result in Lithuania on Tuesday night.
Should that happen then they will stamp their ticket to Germany with time to spare, with a victory being enough to secure them a place at a third successive European Championship.
The Magyars are currently unbeaten in nine matches, including home and away games, and have not lost away from home in over a year - the last defeat came in the UEFA Nations League against Italy in Cesena.
Lithuania Euro Champ Qualifying form:
L
D
L
D
L
W
Lithuania form (all competitions):
D
D
L
D
L
W
Hungary Euro Champ Qualifying form:
W
D
W
W
W
Hungary form (all competitions):
W
D
W
W
D
W
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Team News
A winning starting XI usually remains unchanged for the upcoming match, but with little recovery time in between, Jankauskas may be forced to make some changes to keep his team's legs fresh on Tuesday.
Youngster Gineitis was substituted 20 minutes before the end of regulation time with a slight injury concern, and it remains to be seen if he is ready to play two games in a row, with Edgaras Utkus a possible replacement for him in central midfield.
In this case, Edvinas Girdvainis could take his place in defence, as Lithuania are expected to retain their 3-4-3 formation with three centre-backs.
In addition, Sirvys and Lasickas both had excellent games as wing-backs and will certainly keep their place in Jankauskas's starting XI to provide the same offensive threat from wide areas.
Hungary will have to do without Zsolt Kalmar, who received two yellow cards in injury time against Serbia and was subsequently sent off.
The Fehervar midfielder was brought on after an hour in place of Callum Styles, with the latter now definitely in the starting XI once again to compensate for Kalmar's absence.
Other than that, Hungary are expected to come out in full force against Lithuania to consolidate their first place in Group G.
Vargas, Sallai and Dominik Szoboszlai will form the potent forward trio that has already scored six goals in Euro 2024 qualifying.
Lithuania possible starting lineup:
Zubas; Utkus, Girdvainis, Lekiatas; Lasickas, Sirvys, Gineitis, Vorobjovas; Slivka, Cernych, Paulauskas
Hungary possible starting lineup:
Dibusz; Fiola, Lang, Szalai; Nego, Kerkez, Nagy, Styles; Sallai, Szoboszlai, Varga
We say: Lithuania 1-3 Hungary
Both teams come into this match on the back of wins on Saturday, but the difference between the two teams in terms of group standings and quality of performances is still too obvious to make it an equal match up.