The earth passes directly between the sun and the moon at lunar eclipse.
The earth passes directly between the sun and the moon during a lunar eclipse.
Which preposition is more suitable: at or during ?
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When we talking about time, "at" is used when we are referring to a specific instant or very brief period. "During" is used when we're speaking of a longer time span.
I will arrive at 12:30.
A specific time.
I will arrive during lunch.
Lunch presumably takes a half hour to an hour or so. (Of if you work for the government, several hours. :-)
The battle was fought at the beginning of the Boer War.
At the instant when the war began, or realistically very close to that time.
The battle was fought during the Boer War.
Sometime in the whole period, between when it started and when it ended.
So in this case, a lunar eclipse occurs over a period of time, it's not an instant. So you should say "during a lunar eclipse". If you were talking about one specific instant in this event, you would say at. Like, "... at the moment when the shadow of the Earth is first visible on the lunar disk."