Is it the case that a newly ordained EO priest is supposed to serve the Divine Liturgy each day for the 40 days following his ordination?
This is certainly the tradition, but whether it is strictly observed these days is another matter.
I think there may be some confusions here. The 40 days of Liturgies are celebrated for the 40 days before the Nativity of Christ, and not necessarily by one priest. I only know of a few places (often with multiple priest) where this is able to take place.
There are many people who make this claim for 40 days of liturgies after the ordination, but this would be impossible on many occasions because the days after ordination liturgy would be prohibited (example Great Lent), and I have never heard of one authoritative person ever say it (well that is not true, it was said more as a hazing joke and not to be taken seriously).
The most I have ever seen or heard is a week of liturgies, but more often then not the first liturgy served is the next Sunday.