فَلْيَعْبُدُوا رَبَّ هَٰذَا الْبَيْتِ
The fāʾ at the head establishes a relation of cause and effect between the two preceding verses and this one. What is enumerated across two verses is a favour; what follows from it is a command.
The logic of the sentence is this: you owe something in return to one who looks after you. The sūra does not open this for debate; it takes it as given and moves straight to naming to whom the debt is owed.
The lām at the head of the verb is the lām of command (lām al-amr). In Arabic a command to the second person is given directly ("do"); a command to the third person is given with this lām ("let him do").
There is a point about address here: the sūra does not say "serve", it says "let them serve". The one addressed is not Quraysh directly; it is as though a third eye were looking on from outside. In rhetoric this is approached within the frame of iltifāt (a shift in the direction of address). Its effect is this: the situation of Quraysh is set out like a case at law, and the verdict is delivered not to their faces but into the open. This is a heavier position than a direct rebuke — a person hears the verdict about himself in the third person.
Root ʿ-b-d: service, submission. The concrete sense of the root is a road's being levelled, softened by being trodden over and over; ṭarīqun muʿabbad is a road smoothed by much use. Worship, then, is a turning that has been softened by repetition, whose resistance has been broken.
This root has a hidden kinship with the root of īlāf: both convey a state that forms through repetition. Quraysh were made used to an order of travel (īlāf); the return asked of them is likewise a habit (ʿibāda). The sūra asks that habit be answered with habit.
First: not the House, but the Lord of the House. Quraysh already revered the Kaʿba; they counted themselves its servants and lived on the standing it gave them. The sūra does not reject their attachment; it corrects its target: not the building, but the Owner of the building.
This is the exact name of a very common displacement in religious life. A person becomes attached to the means of the sacred, and in time begins to take the means for the thing itself. Place, ceremony, title, institution — all exist in order to point somewhere; and all can take the place of what they point to. The correction the sūra makes is a single word: Rabba.
Second: "this" House. Hādhā is a demonstrative, and it indicates what is near — near enough to be pointed at. The sūra is not framing an abstract theological sentence; it is pointing at the building visible from the window of the one addressed.
Its persuasive value is high. Quraysh are not asked to believe something they do not accept; they are asked to see the consequence of what they do accept. The argument works in this form: You already believe this House has a Lord — indeed you relied on Him when Abraha came. Then let your service be to Him too.
The same demonstrative is used of the city in a nearby sūra: "and this secure land" (al-Tīn 95/3). In both, what is indicated stands before the eyes of the one addressed.
Third: why not "your Lord"? The sūra could have said "let them serve their Lord". It does not. It builds the link not through the people but through the House. The reason is probably this: the identity of Quraysh was bound to that House; their standing, their income, their position against the surrounding tribes came from there. The sūra takes hold of precisely that point of support and pulls upward from it.
"The first House established for people is surely the one at Bakka, blessed and a guidance for all beings… Whoever enters it is safe" (Āl ʿImrān 3/96-97).
"And when We made the House a place of return for people, and a safety" (al-Baqara 2/125).
In both verses the House is named together with safety. The same will happen in the fourth verse of Sūrat Quraysh. The Qurʾān's own definition of the House overlaps with the definition of the favour this sūra gives.