It depends: are we talking about the university or the cathedral? Different pronunciations

The Fighting Irish school is said differently than the Paris Cathedral? They are said differently

They are the same name, i.e, Our Lady, referring to the Virgin Mary. Both are founded/built by French priests and should technically be pronounced the French way. It is just the case that in the US it’s pronounced with an American accent, similar to many other French named cities in Indiana!!

Depends on if you’re from Indiana or the rest of the world.

In french

Not ra Dame (as in lamb)

The same way I pronounce Houston, Chili, Reading