I have run into various bits of this story at different times. My ex-wife's family lived across the street from the chapel in Trsat where the house is supposed to have touched down. On one occasion I was there while they were preparing for an imminent visit by Pope JP2 (and not making an epic effort for it). It's cluttered with weird votive offerings from people who'd benefited from miracles - discarded crutches, paintings of ships saved from storms and so on. A local thing is climbing up the 561 stairs from Rijeka down below, on your knees, but nobody seems to have done it for a generation.

https://en.m.wikipedia.org/wiki/Petar_Kružic_staircase

Around 1500 the Pope decided to make the Holy House into a pan-European cult, and sent stones from it to be the foundation stones of "Loreto chapels". One of them was sent to Musselburgh just east of Edinburgh and they built a chapel there - the name still survives attached to the posh Loretto School. But come the Reformation in 1560, the people of Musselburgh smashed the chapel into unidentifiable bits and recycled it all into walls and buildings around the town. The Holy House stone could be anywhere. The Pope at the time excommunicated the whole of Musselburgh. I doubt they were very impressed.

The litany now sung arose rather late in the game, 1558 at the earliest:

https://en.m.wikipedia.org/wiki/Litaniae_lauretanae

Or perhaps better:

https://la.m.wikipedia.org/wiki/Litaniae_Lauretanae

Mozart set it to music as a young man. Not one of his more memorable compositions. I don't think there was originally specific tune for it - if it got to Portugal at the time it was written I suppose it might well have been sung to a sailors' song. If it got to Musselburgh in time it might have been sung to a sledgehammer demolition shanty.