« لَآ أُقْسِمُ »: "No! I swear"
The formula « لَآ أُقْسِمُ » opens an oath by first rejecting what the opponents say. It does not mean "I do not swear": the لَا is a "No!" dismissing their claim, and then comes the oath. It is rendered everywhere "No! I swear by …".
The formula occurs eight times, in seven sentences (56:75, 69:38, 70:40, 75:1, 75:2, 81:15, 84:16, 90:1).
The text itself shows that it is indeed an oath, not its refusal. In 56:75-76, after « فَلَآ أُقْسِمُ بِمَوَٰقِعِ ٱلنُّجُومِ », it adds at once: « وَإِنَّهُۥ لَقَسَمٌۭ لَّوْ تَعْلَمُونَ عَظِيمٌ », "and indeed, it is a great oath, if you but knew". If لَا negated the oath, that sentence would make no sense.
The لَا is therefore a reply: it rejects the opposing claim (the denial of the Day, of the Recitation, of the Return), and then the oath establishes the truth. The same construction appears in 4:65: « فَلَا وَرَبِّكَ », "But no, by your Guardian!". The translation keeps both steps, separated by the exclamation mark: "No! I swear".
In the text
فَلَآ أُقْسِمُ بِمَوَٰقِعِ ٱلنُّجُومِ وَإِنَّهُۥ لَقَسَمٌۭ لَّوْ تَعْلَمُونَ عَظِيمٌلَآ أُقْسِمُ بِهَٰذَا ٱلْبَلَدِلَآ أُقْسِمُ بِيَوْمِ ٱلْقِيَٰمَةِ