In general, Orthodox do not object to Marian apparitions per se--there have been many such in the lives of the saints. But of course, such apparitions must be tested--they must conform to the Faith once for all delivered to the saints.
While the Orthodox Church has not formally anathematized the dogma of the Immaculate Conception, it is true that IC does go against Orthodox teaching on the nature of grace, free will, human nature, soteriology, etc. Thus, if IC is inseparable from the Lourdes apparition, then Orthodox would say that the Lourdes apparition could not be genuine.
Miracles alone do not validate a teaching or practice--everything must conform to the Faith once for all delivered to the saints. Miracles may be demonic (Satan masquerades as an angel of light, the demonized servant girl of Acts, etc.). They may also simply be God's gracious condescension and not at all an authentication of a teaching or practice.