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There are academic journals on this topic, but I no longer have access to JSTOR or the others.
The NPS cites that her looks are said to be of his mother, but that is incorrect, perhaps whitewashing.
https://www.thebattery.org/lady-liberty-10-fascinating-facts/
The original model may have been an Egyptian woman
Many historians say that the Statue of Liberty was modeled after Libertas, the Roman goddess of freedom. However, sculptor Frédéric-Auguste Bartholdi was first inspired by the colossal figures guarding Nubian tombs. He developed a lifelong passion for large-scale public monuments. In his proposal for the Suez Canal, Bartholdi designed a monumental statue of a robe-clad woman representing Egypt to stand at Port Said, at the northern end of the canal. A prototype for the statue was titled “Egypt Carrying the Light to Asia.”
https://www.britannica.com/story/who-was-the-woman-behind-the-statue-of-liberty
Bartholdi’s journey to Egypt was enormously transformative and influential. In 1868 he returned to marvel again at the Colossi, and in 1869 Bartholdi submitted a colossal statuary proposal to the Egyptian khedive, Ismāʿīl Pasha. Bartholdi hoped that the khedive would use his sculpture design to commemorate the completion of the Suez Canal, which had opened that year. As the shortest path between the Mediterranean and Red Seas, the Suez Canal functioned as a literal sea-bridge between Europe and Asia. If selected, Bartholdi hoped that his colossus would be seen as a symbol of cultural progress and understanding.
Bartholdi’s design for the khedive was modeled after a woman fallāḥ, or Egyptian peasant. Unfortunately, very little is known about this fallāḥ besides her socioeconomic status; Bartholdi left no records that indicate any interest in her personal story. Despite this, selecting a woman was no accident. Bartholdi was conscious of a centuries-long European artistic tradition of personifying values, ideas, and even countries in the forms of women. These personifications were venerated and sometimes worshipped, but of particular importance for Bartholdi was that they lived and lingered in the minds of those who viewed their likenesses. This logic is clear in the name, form, and function of Bartholdi’s contest submission. Titled Egypt Carrying the Light to Asia, this colossal woman was to be positioned in the middle of the Suez Canal atop a monumental plinth. Dressed in what Egyptians would have recognized as the clothes of a fallāḥ and immortalized as a monument, she would have been a point of pride for Egyptians of all social classes. She doubled as a lighthouse, holding a torch up high and radiating light from her head. As ships from countless nations passed beneath her, this woman was to be seen as the physical embodiment of Egypt and its progress.
Although Bartholdi’s submission may have impressed the khedive, building the colossus would have been enormously expensive. Egypt was facing financial problems that likely caused the khedive to shift his attention elsewhere, and the project was terminated. But if Bartholdi’s colossal fallāḥ seems recognizable, that is because he was determined to repurpose his scrapped design. Between 1870 and 1871, he began to alter the details of his sketches. The woman’s characteristic Egyptian dress gave way to Greek robes, and light beamed from her torch instead of her head. A diadem would later replace her head covering, while her left hand soon bore a tablet. But like the sketches from 1869, she still held her torch with an upstretched arm, her other limb positioned at her waist. Beneath what would become America’s Liberty Enlightening the World was Egypt’s own colossal fallāḥ, still “carrying the light.”
https://www.smithsonianmag.com/smart-news/statue-liberty-was-originally-muslim-woman-180957377/
The statue’s designer, Frédéric-Auguste Bartholdi, was also French, but he found inspiration in a very different place: Egypt. In 1855, he visited Nubian monuments at Abu Simbel, which feature tombs guarded by gigantic colossus figures. Bartholdi became fascinated by the ancient architecture, developing what the National Park Service calls a “passion for large-scale public monuments and colossal structures.” Eventually, he channeled that passion into a proposal for the inauguration of the Suez Canal.
Bartholdi envisioned a colossal monument featuring a robe-clad woman representing Egypt to stand at Port Said, the city at the northern terminus of the canal in Egypt. To prep for this undertaking, Barry Moreno, author of multiple books about the statue, writes that Bartholdi studied art like the Colossus, honing the concept for a figure called Libertas who would stand at the canal.
“Taking the form of a veiled peasant woman,” writes Moreno, “the statue was to stand 86 feet high, and its pedestal was to rise to a height of 48 feet.” Early models of the statue were called “Egypt Carrying the Light to Asia.”
Edward Berenson, author of Statue of Liberty: A Translatlantic Story, writes that Bartholdi’s concept morphed from “a gigantic female fellah, or Arab peasant” into “a colossal goddess.” But Egypt, which had invested enormous amounts of time and money into the landmark canal, was not as eager about Bartholdi’s idea. Isma’il Pasha, the reigning khedive, rejected the plan as too costly.
Conceptually, how would that go over in Egypt to have a French woman grace a statue at the Suez canal?
He also approached a couple of other countries after Egypt turned him down to see if they wold like it, which is mot mentioned in these articles.
When he could not find any country wanting of the statue, it was repurposed.
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= new reply since forum marked as read
Then, continuing the island tour, maybe they can take him to Rikers island, where he really belongs. 
