I think we should take them on a case-by-case basis. Our Lady of Lourdes, for example, is said to have confirmed the Roman Catholic teaching of the Immaculate Conception, so I wouldn’t think it appropriate to venerate this particular one…
I used to be very devoted to Our Lady of Lourdes when I was Catholic so it is a little difficult for me, though.

One of my favourites is Our Lady of Zeitoun (at a Coptic Church in Egypt).