Attention: I'm not a teacher.
Hi jesson cui,
Generally speaking there are the following synonyms of the word in question. I am unable to give a definite answer under given conditions. There is no a synonymous context in your inquiry.
airy (adj.) = SYNONYMS
airy, diaphanous, ethereal, filmy, gauzy, gossamer, sheer, transparent, vaporous. These adjectives mean so light and insubstantial as to resemble air or a thin film:
airy curtains blowing at the window; a diaphanous veil; ethereal mist; the filmy wings of a moth; gauzy clouds in the sky; a gown of gossamer fabric; sheer silk stockings; transparent chiffon; vaporous shadows at dusk.
For example I know one term that is close to that one in your original post (Luftmensch). namely “airy fairy”.
airy fairy

= One that is insubstantial or impractical:
“They'd wanted him for Ambassador in Paris but he'd turned it down; he'd no patience with the airy-fairies”
airy (adj.)
insubstantial or impractical:
“You are talking about some airy fairy concept which will never come in my lifetime”
In German language:
aus der Luft gegriffen, (inf.) hübsch
There is another expression in English language:
In an airy manner; lightly; gaily; jauntily;
Regards.
V.