The Greek island, where hundreds of thousands of asylum-seekers and other migrants have arrived in recent months, is on the frontline of a humanitarian crisis that has sparked disagreements between European countries and brought the bloc's system of open borders to the brink of collapse.
The island has also become the focus for criticism of the EU's March deal to ensure so-called economic migrants who travel to the Greek islands on boats operated by people smugglers are quickly sent back to Turkey, which has agreed to take them in return for billions in EU cash.
"Perhaps (the Pope) can help open the borders?" Nedal, a 35-year-old Syrian being looked after with his family by Catholic aid group Caritas, told AFP ahead of the visit.
The two religious leaders, accompanied by Archbishop Ieronymos, the head of the Church of Greece, will spend five hours on Lesbos where they will visit the Moria processing centre.
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The facility, currently housing around 3,000 people, has been described as a centre for "arbitrary detention" by rights groups. Amnesty International has urged the pope to use his time on Lesbos to speak out against the EU-Turkey deal concluded last month.
The pontiff, however, has demonstrated in the past that he is not one to mince his words and his spokesman reiterated: "If he the pope has something to say he will say it."
Francis said earlier this week that the goal of his trip was "to show closeness and solidarity with the refugees as well as the citizens of Lesbos and to all the Greek people who have been so generous in their welcome".
And that line has been backed by Bartholomew, the Turkey-based leader of the world's Orthodox Christians, who said Europe as a whole must display the same generosity as the people of Lesbos.
"This offends God himself," he said. "The segregation of certain groups of people to the advantage of others does not reflect His desire.