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yes, the white king/queen can lose a tempo
"Lose a tempo"? What does that mean? I think that position could be possible if Black moved one of his knights, and then put it back where it was. But I see no other way.
"Lose a tempo" is more or less "change side to move".
The key thing about the position is that it is black to move, and after the obvious e3 Nf6 d3 Ng8 you have the position but with white to move. Famously, knights cannot lose tempi, but the white king/queen can triangulate to acieve this as shown by chaotic_iak
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