Do the Orthodox recognize Western saints such as Saint Therese of Lisieux?
Orthodox Christians recognizes that people like Saint Therese, or Saint Ignatius, or Saint Angela are saints of the Roman Catholic Church. However, they are not seen as as Orthodox saints.
When the Church (through a bishop, synod or patriarch) proclaims someone to be a saint, it presents that person’s life as an example for others, a measure against which we may choose to measure our lives. This is why the term “canonization” exists (although the Orthodox expression tends to be “glorification” rather than “canonization.” A canon is a rule or measuring stick, so by canonizing someone’s life, the Church presents it as a reference for others.
When the Roman Catholic Church canonized Saint Therese, it presented to the faithful an example of a spiritual path to follow. This spiritual path, however, differs from that of Orthodox saints. There are certain beliefs promoted by the Roman Catholic Church as beneficial or mandatory that the Orthodox consider to be erroneous or possibly detrimental to one’s salvation. This is why we recognize that Saint Therese is in fact a Roman Catholic saint, but Orthodoxy cannot, obviously, recommend her entire life or belief system as an example for Orthodox Christians to follow. These are Christians that have lived outside the boundary of the Orthodox communion and for which Orthodox bishops cannot make formal proclamations, even if their piety or martyrdom are worthy of respect.
Finally, the reciprocal situation exists: the Roman Catholic Church does not formally recognize Orthodox saints and could not do so for the same reasons explained above.
For further readings on some of the differences between Roman Catholic and Eastern Orthodox spirituality, cf. Fr. Sergei Sveshnikov “Imagine that: Mental Imagery in Roman Catholic and Eastern Orthodox Private Devotion.”