Marco Rossi's men could only play out a goalless game with Montenegro on Saturday, while 10-man Lithuania held on for a 1-1 draw with Bulgaria.
Match preview
Dominik Szoboszlai could not inspire Hungary to win in Montenegro as both sides settled for a point in Podgorica.
Maximum points would have taken the away side level on six points with table-topping Serbia, but they sit joint-second with the Brave Falcons.
Despite dominating possession, Rossi's troops did not fashion clear chances, and the point was deserved after 90 minutes.
Facing Lithuania appears straightforward on paper, with Tuesday's visitors on one point after two games, but Magyarok still have to earn the points in Budapest.
Matches at the Puskas Arena in Euro qualifying often end in Hungary's favour, underlined by seven wins from eight since October 2015.
That impressive home run means Lithuania face an uphill task to secure their first victory at the third time of asking.
Edgaras Jankauskas's team could only draw with Bulgaria on Saturday, an outcome that leaves them level with Group I's bottom side.
However, it will be remiss not to mention that Lithuania played over 70 minutes with 10 men after Justas Lasickas received a 17th-minute red card against the Bulgarians.
Marin Petkov levelled for the away side in minute 27, but Jankauskas's troops held on despite being short-handed for most of the game.
Even though Lithuania receive full marks for the defensive shift after the interlude, they risk falling six points back of Hungary if they are beaten in Budapest.
Hungary Euro Champ Qualifying form:
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D
Hungary form (all competitions):
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Lithuania Euro Champ Qualifying form:
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D
Lithuania form (all competitions):
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Team News
With no injuries to report or suspensions from their Montenegro clash, Hungary could lean on a similar line-up to the side that played a goalless encounter on Saturday.
Szoboszlai is the team's talisman, and the RB Leipzig man is expected to be one of the number 10s in Rossi's 3-4-2-1.
With Lasickas suspended after his early dismissal against Bulgaria, Jankauskas has to make a change at right-back.
Lithuania captain Fedor Cernych also went off injured in minute 38, possibly forcing the Lithuania boss into a change up top if Tuesday's game comes too soon for the centre-forward.
Hungary possible starting lineup:
Dibusz; Lang, Orban, Szalai; Bolla, Nagy, Styles, Kerkez; Szoboszlai, Sallai; Adam
Lithuania possible starting lineup:
Gertmonas; Sirvys, Lekiatas, Girdvainis, Beneta; Vorobjovas, Verbickas; Sesplaukis, Gineitis, Jankauskas; Paulauskas