Le Pen's meeting with Aoun will be the first time she has been officially received by a foreign leader since taking over the party leadership from her father, Jean-Marie, in 2011.
Her National Front (FN) party hopes it will show she is taken seriously abroad, following a number of disappointments in that field.
The Lebanese leaders have already met centrist candidate Emmanuel Macron and would have met mainstream right presidential candidate François Fillon had he not cancelled his visit because of the Penelopegate scandal.
Links with Christian right
The visit to Lebanon, to which thousands of refugees from Syria's civil war have fled, is a sign that she "is tremendously interested in this region", FN treasurer Wallerand de Saint Just told the AFP news agency.
Le Pen has had a number of setbacks in her attempts to gain credibility on the international plane:
- In the US, despite her enthusiastic welcome of Donald Trump's election victory, he did not meet her when she went to the country in January, even though she was spotted in the lobby of Trump Tower in New York;
- In Canada all parties in Quebec refused to meet her when she visited the French-speaking province in 2016;
- Germany's Chancellor Angela Merkel has ruled out seeing her;
- Spain's Prime Minister Mariano Rajoy has said her election would be a "catastrophe";
- Poland's Foreign Affairs Minister Witold Waszczykowski did meet her for an hour and a half when he visited Paris in January, commenting afterwards that her plans for the European Union would be "harmful";
- Russia's President Vladimir Putin did not meet her, not even in private, she was obliged to declare after a former foreign policy adviser, Euro-MP Aymeric Chauprade, hinted that he had.
It will also be a gesture of support for oriental Christians, facing persecution by Islamic fundamentalists in Iraq, Syria and Egypt, a cause also championed by Fillon.
The FN has longstanding links with right-wing Christian parties in a country whose sectarian divides led to civil war in 1975-1990.
Some members fought alongside Christian militias to defend "Western values" against "revolutionary Islamic terrorism", in the words of one of them, Thibault de la Tocnaye, who is a member of Le Pen's election campaign team.
Differences over Syria
Aoun, a former general who leads the Maronite Christian Free Patriotic Movement, shares power with Hariri, the head of the largely Sunni-Muslim Future Movement, in a constitutional arrangement that divides posts along confessional lines.
Although he fought Syrian troops in 1989 and fled Lebanon for France when they returned in 1990, Aoun has now formed an alliance with Damascus's main Lebanese ally, the Shia-Muslim Hizbullah.
So he should see eye to eye with Le Pen, who backs President Bashar al-Assad in the Syrian war.
But Hariri, whose party is part of the 14 March Alliance which forced Syrian troops out of Lebanon and holds Assad responsible for his father's assassination, would not agree with the FN's line.
Nor would some of the party's longstanding allies on the Christian right, for example Samir Geagea, a former militia leader who served jail time for several assassinations during the civil war, whom she is scheduled to meet on Tuesday.
Another of Le Pen's policies that has not gone down well with Lebanese Christians, or at least with those who have both French and Lebanese nationality, is her opposition to dual nationality for non-Europeans.
"That threatens to stir up a major row," the founder of the FN-Liban group, Maria Jallard, told Le Monde newspaper. "Unless she announces an exception for Christians."