What is the relation between the oath by the piercing star and this response?

The answer is: The word (protector) either has a meaning of giving love and care from the conservator to the conserved or it means the watcher who does not miss anything at all.

Considering the first meaning, Allah (swt) says:

{ لَهُ مُعَقِّبَاتٌ مِّن بَيْنِ يَدَيْهِ وَمِنْ خَلْفِهِ يَحْفَظُونَهُ مِنْ أَمْرِ اللَّهِ }

(For each one are successive [angels] before and behind him who protect him by the decree of Allah.) (Ar-Ra’d: 11)

This protection is by the command of Allah (swt) as that a human being may passes through various trials that he is incapable of avoiding or escaping of them. Thus, when he is saved of them, he would say that “These are divine matters and I have no power to face them but I was saved by the wills of Allah (swt)”.  This means that this man has been protected by something that is beyond his power by Allah’s (swt) wills.

On the other hand, the meaning of surveillance is derived from the is indeicated in this verse:

 {وَإِنَّ عَلَيْكُمْ لَحَافِظِينَ % كِرَامًا كَاتِبِينَ % يَعْلَمُونَ مَا تَفْعَلُونَ }

(And indeed, [appointed] over you are keepers, %  Noble and recording; % They know whatever you do..) (Al-Infitar: 10-12)

لَمَّا (but): This Arabic word has many purposes. Of them, is to negate the past verb. But this negation is connected with the present with the possibility that this action may or expected to happen in the future as in this verse:

 {قَالَتِ الْأَعْرَابُ آمَنَّا ۖ قُل لَّمْ تُؤْمِنُوا وَلَٰكِن قُولُوا أَسْلَمْنَا وَلَمَّا يَدْخُلِ الْإِيمَانُ فِي قُلُوبِكُمْ }

(The bedouins say, “We have believed.” Say, “You have not [yet] believed; but say [instead], ‘We have submitted,’ for faith has not yet entered your hearts…) (Al-Hujurat: 14)

This word is also used as an article to indicate the occurrence of something as a result of another one. Allah (swt) says:

{  فَلَمَّا ذَهَبَ عَنْ إِبْرَاهِيمَ الرَّوْعُ وَجَاءَتْهُ الْبُشْرَىٰ يُجَادِلُنَا فِي قَوْمِ لُوطٍ}

(And when the fright had left Abraham and the good tidings had reached him, he began to argue with Us concerning the people of Lot.) (Hud: 74)

As we say for example: When someone such and such came, we made so and so food.

So, our making of food is up for the coming of someone such and such.

This third usage of this article is, as in our recent verse, to express an exception. In this case the meaning is: “No single soul but that it has over it a protector”.

Let’s ponder upon the accuracy of the Quranic expressions in generalizing the self-accounting; the word (soul) in this verse is general but the generalization is increased by the word (every) to emphasize that every soul is watched, first of all, from Allah (swt) then by the angels who take turns recording the deeds and following the humans’ actions.