
ein Amt niederlegen
to resign
To voluntarily step down from an official position or office.
Der Minister hat nach dem Skandal sein Amt niedergelegt.
The minister resigned from his office after the scandal.
to lay down / resign
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to resign
To voluntarily step down from an official position or office.
Der Minister hat nach dem Skandal sein Amt niedergelegt.
The minister resigned from his office after the scandal.

to stop work
To deliberately stop working in order to protest or go on strike.
Die Belegschaft legte für 24 Stunden die Arbeit nieder, um für höhere Löhne zu demonstrieren.
The workforce stopped work for 24 hours to demonstrate for higher wages.

to lay down
To place something in a particular place, often with a certain amount of care or ceremony.
Die Trauernden legten am Mahnmal einen Kranz nieder.
The mourners laid a wreath down at the memorial.

to set down
To record thoughts, rules, or agreements in writing. This use is rather formal.
Die Grundsätze des Unternehmens sind im Leitbild niedergelegt.
The company's principles are set down in its mission statement.

to lie down
To lie down to sleep or rest. This use is rather formal or literary.
Nach dem langen Marsch legten sich die Wanderer erschöpft nieder.
After the long march, the hikers lay down exhausted.
'Niederlegen' (to lay down / resign) is a separable verb. In a main clause in the present tense or simple past, the prefix 'nieder' comes at the end of the sentence. In subordinate clauses and in the infinitive, the verb stays together.
Er legt den Stift auf dem Schreibtisch nieder.
He lays the pen down on the desk.
The verb is made up of 'nieder' (an old form meaning 'down') and 'legen' (to lay). The basic meaning 'to lay something down' can be found in all uses, whether it is about an object, an office, or work.
Der König legte seine Krone nieder.
The king laid down his crown.
The object of the verb reveals the exact meaning. 'Ein Amt niederlegen' means to resign. 'Die Arbeit niederlegen' means to go on strike. 'Einen Kranz niederlegen' is a ceremonial act.
Die Mitarbeiter drohten damit, die Arbeit niederzulegen.
The employees threatened to stop work.
The meaning 'to resign' is used almost exclusively with the object 'Amt' (office) or a specific position such as 'Mandat' (mandate/seat). The expression is 'ein Amt niederlegen' (to resign from an office).
Die Bürgermeisterin legte überraschend ihr Amt nieder.
The mayor unexpectedly resigned from her office.
In the meaning 'to record in writing', 'niederlegen' (to set down) is very formal and is used mainly in administrative or legal language. It implies that something is documented officially and permanently.
Die Bedingungen des Vertrags wurden schriftlich niedergelegt.
The terms of the contract were set down in writing.
To express that you lie down in order to sleep or rest, the reflexive form 'sich niederlegen' (to lie down) is used. This form is rather elevated or literary.
Nach einem anstrengenden Tag legte er sich früh nieder.
After a tiring day, he lay down early.
to hire / adjust / stop
Both verbs can mean that work is coming to an end. However, „die Arbeit niederlegen“ usually emphasizes that people are deliberately protesting or going on strike, whereas „die Arbeit einstellen“ can also neutrally refer to ending an activity. Use „niederlegen“ for protests and „einstellen“ for an ordinary ending.

Die Beschäftigten legen die Arbeit nieder, um gegen die geplanten Kürzungen zu protestieren.
The employees are stopping work to protest the planned cuts.
Das Unternehmen stellt die Produktion wegen geringer Nachfrage vorübergehend ein.
The company is temporarily halting production because of low demand.