lüften
to air
To let fresh air into an enclosed room by opening windows or doors.
Ich muss dringend mal das Schlafzimmer lüften, hier ist ganz schlechte Luft.
I really need to air out the bedroom; the air in here is terrible.

to air / reveal / lift
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to air
To let fresh air into an enclosed room by opening windows or doors.
Ich muss dringend mal das Schlafzimmer lüften, hier ist ganz schlechte Luft.
I really need to air out the bedroom; the air in here is terrible.

The verb 'lüften' (to air) is derived directly from the noun 'die Luft' (air). All meanings have to do with 'Luft' (air) or creating free space, whether literally or figuratively.
Kannst du bitte kurz das Fenster öffnen und lüften?
Could you please open the window briefly and air the room out?
The object of the verb reveals the exact meaning. You air 'ein Zimmer' (a room) for fresh air, reveal 'ein Geheimnis' (a secret), or tip 'einen Hut' (a hat) as a greeting.
Er lüftete den Vorhang, um aus dem Fenster zu sehen.
He lifted the curtain to look out the window.
In the meaning 'frische Luft hereinlassen' (to let fresh air in), 'lüften' (to air) is typically used with rooms or textiles. Common combinations are 'das Zimmer lüften' (to air the room), 'die Wohnung lüften' (to air the apartment), or 'die Betten lüften' (to air the beds).
Nach dem Kochen sollten wir die Küche gut lüften.
After cooking, we should air the kitchen out well.
The figurative meaning is used almost exclusively in fixed expressions. The most common are 'ein Geheimnis lüften' (to reveal a secret) and 'ein Rätsel lüften' (to solve a mystery).
Die Polizei hofft, das Rätsel des Falles bald lüften zu können.
The police hope to be able to solve the mystery of the case soon.
The expression 'den Hut lüften' (to tip one's hat) describes a traditional gesture of greeting or respect, now rather rare, that was mainly performed by men.
Er lüftete kurz seinen Hut, als er den Direktor traf.
He briefly tipped his hat when he met the director.
to lose weight / decrease / take off
'abnehmen' and 'lüften' can both have to do with a movement upward or away from something. 'abnehmen' means that you remove something completely, for example a hat, a lid, or a picture from the wall. 'lüften' here usually means that you lift something only slightly, often briefly and not completely. With a hat, there is a fixed expression: 'den Hut lüften' (to tip one's hat) as a greeting or sign of respect. The words can be confused because both can be used with clothing or objects on the body. The important point is: 'abnehmen' removes something completely; 'lüften' only lifts it briefly or slightly.

Der alte Herr lüftet kurz den Hut, als er die Nachbarin grüßt.
The old gentleman briefly tips his hat as he greets the neighbor.
Zu Hause nimmt sie den nassen Hut ab und hängt ihn an die Tür.
At home, she takes off the wet hat and hangs it on the door.