Lukaku headed the opener from Jeremy Doku's cross before Eddy Pascual was shown a second yellow card for a foul on the Roma striker, who is on loan from Chelsea.
The 30-year-old completed his hat-trick by the half-hour mark and grabbed his fourth after 37 minutes before being substituted at half-time. Arsenal forward Leandro Trossard completed the rout late on.
Lukaku's total of 14 goals is a record for a European Championship qualifying campaign, beating the mark of 13 set by Northern Ireland's David Healy in 2008 and equalled by Poland's Robert Lewandowski in 2016.
Belgium had already booked their place at next year's tournament and the win saw them finish top of Group F ahead of Austria.
Sweden, who could not qualify, beat Estonia 2-0 in the group's other fixture.
Serbia qualified for Euro 2024 with a 2-2 draw with Bulgaria in Group G, where group winners Hungary beat Montenegro 3-1 thanks to a brace from Liverpool midfielder Dominik Szoboszlai.
Serbia only needed a point or for Montenegro not to beat Hungary to secure their berth in Germany, but that looked a distinct possibility when they trailed 2-1 and Montenegro led 1-0 in Budapest.
However, Serbia's Srdan Babic equalised in the 82nd minute and Szoboszlai scored twice in the space of two minutes in the second half to turn Hungary's game around.
Scotland concluded their successful campaign with an action-packed 3-3 draw with Norway at Hampden Park.
Steve Clarke's men twice came from behind before Stuart Armstrong gave the home side the lead just before the hour mark, but Norway substitute Mohamed Elyounoussi levelled in the 86th minute.
Group A winners Spain beat Georgia 3-1 in Valladolid.
Portugal ended their qualifying campaign with a 10th straight win as goals from Bruno Fernandes and Ricardo Horta gave them a 2-0 victory over Iceland.
Group J runners-up Slovakia enjoyed a 2-1 win over 10-man Bosnia and Herzegovina, who will join Luxembourg in the play-offs.
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