During an interview and cooking demonstration with Andre Soltner, he was asked the meaning of the word Lutece. Soltner was the chef/proprietor of the restaurant Lutece, in New York City for 34 years. He was most happy to explain that the word came from the first name of Paris, which was Lutetia. He used this word, with some originality of his own, to name his establishment.

The Romans conquered the Paris Basin in 52 BC and, after making the island a garrison camp, began extending their settlement in a more permanent way to Paris's Left Bank. The Gallo-Roman town was originally called Lutetia (more fully, Lutetia Parisiorum, "Lutetia of the Parisii"). It became a prosperous city with a forum, baths, temples, theatres, and an amphitheatre.

By the end of the Western Roman Empire, the town was known as Parisius, a Latin name that would later become Paris in French. Christianity was introduced in the middle of the 3rd century AD by Saint Denis, the first Bishop of Paris: according to legend, when he refused to renounce his faith before the Roman occupiers, he was beheaded on the hill which became known as Mons Martyrum (Latin "Hill of Martyrs"), later "Montmartre", from where he walked headless to the north of the city; the place where he fell and was buried became an important religious shrine, the Basilica of Saint-Denis, and many French Kings are buried there.

More Info: en.wikipedia.org