So many lives and deaths had been measured in this battle. Had the balance of the odds tipped slightly against them—everything could have been lost. That was something he had never taught any of his students at the Academy—how much victory depended on luck as well as skill.
I don't think the meaning is
... how much victory depened on luck and skill.
Maybe it means
of course skill was important but victory needed luck as well.
He had taught that victory depends on skill but now realizes that luck is also essential, perhaps even more essential.
"On luck as well as skill" means "on luck in addition to skill" or "not just on skill, but also on luck".
You can interpret the sentence in this way:
That was something he had never taught any of his students at the Academy—how much victory depended on luck as well as [how much victory depended on] skill.
This is an example of elision in a parallel sentence structure. It's assumed that how much victory depended on applies to both luck and skill—and in order to simplify the sentence, that phrase is removed in the second instance.
So, your interpretation is correct. Victory depends on both skill and luck. (But he had only taught about it depending on skill in the past.)
how much victory depended on [luck] [as well as skill].
It's very simple.
This is the idiomatic use of "as well as", meaning approximately "and", "in addition to".
"As well as" behaves here like the coordinator "and". It links the bracketed noun phrases, a property characteristic of coordinators.
Thus idiomatic "as well as" is best reanalysed as a compound coordinator.
